Diffusion and osmosis

WEBVTT
Kind: captions
Language: en

00:00:00.450 --> 00:00:02.550
In this video, I want to
cover several topics

00:00:02.550 --> 00:00:03.650
that are all related.

00:00:03.650 --> 00:00:05.850
And on some level, they're
really simple, but on a whole

00:00:05.850 --> 00:00:07.883
other level, they tend to
confuse people a lot.

00:00:07.883 --> 00:00:10.110
So hopefully we can
make some headway.

00:00:10.110 --> 00:00:12.400
So a good place to start-- let's
just imagine that I have

00:00:12.400 --> 00:00:15.460
some type of container here.

00:00:15.460 --> 00:00:18.130
Let's say that's my container
and inside of that container,

00:00:18.130 --> 00:00:21.430
I have a bunch of
water molecules.

00:00:21.430 --> 00:00:24.070
It's just got a bunch
of water molecules.

00:00:24.070 --> 00:00:25.550
They're all rubbing against
each other.

00:00:25.550 --> 00:00:27.920
It's in its liquid form,
this is liquid water.

00:00:27.920 --> 00:00:30.340
and inside of the water
molecules, I

00:00:30.340 --> 00:00:33.050
have some sugar molecules.

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Maybe I'll do sugar in
this pink color.

00:00:35.790 --> 00:00:40.690
So I have a bunch of sugar
molecules right here.

00:00:40.690 --> 00:00:43.040
I have many, many more water
molecules though.

00:00:43.040 --> 00:00:44.290
I want to make that clear.

00:00:49.420 --> 00:00:55.660
Now in this type of situation,
we call the thing that there's

00:00:55.660 --> 00:01:00.440
more of, the solvent.

00:01:00.440 --> 00:01:03.350
So in this case, there's more
water molecules and you can

00:01:03.350 --> 00:01:07.990
literally just view more as
the number of molecules.

00:01:07.990 --> 00:01:10.010
I'm not going to go into a whole
discussion of moles and

00:01:10.010 --> 00:01:13.140
all of that because you may or
may not have been exposed to

00:01:13.140 --> 00:01:15.670
that yet, but just imagine
whatever there's more of,

00:01:15.670 --> 00:01:17.740
that's what we're going
to call the solvent.

00:01:17.740 --> 00:01:24.630
So in this case, water
is the solvent.

00:01:24.630 --> 00:01:30.030
And whatever there is less of--
in this case, that is the

00:01:30.030 --> 00:01:32.730
sugar-- that is considered
the solute.

00:01:36.292 --> 00:01:37.640
It doesn't have to be sugar.

00:01:37.640 --> 00:01:40.320
It can be any molecule that
there's less of, in the water,

00:01:40.320 --> 00:01:41.570
in this case.

00:01:45.750 --> 00:01:49.620
And we say that the sugar has
been dissolved into the water.

00:02:03.500 --> 00:02:06.420
And this whole thing right here,
the combination of the

00:02:06.420 --> 00:02:10.229
water and the sugar molecules,
we call a solution.

00:02:10.229 --> 00:02:14.140
We call this whole
thing a solution.

00:02:14.140 --> 00:02:16.870
And a solution has the solvent
and the solute.

00:02:16.870 --> 00:02:18.160
The solvent is water.

00:02:18.160 --> 00:02:21.110
That's the thing doing the
dissolving and the thing that

00:02:21.110 --> 00:02:23.220
is dissolved is the sugar.

00:02:23.220 --> 00:02:24.290
That's the solute.

00:02:24.290 --> 00:02:27.950
Now all of this may or may not
be review for you, but I'm

00:02:27.950 --> 00:02:32.870
doing it for a reason-- because
I want to talk about

00:02:32.870 --> 00:02:34.370
the idea of a diffusion.

00:02:39.960 --> 00:02:43.490
And the idea is actually
pretty straightforward.

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If I have, let's say,
the same container.

00:02:46.790 --> 00:02:49.600
Let me do it in a slightly
different container here, just

00:02:49.600 --> 00:02:50.640
to talk about diffusion.

00:02:50.640 --> 00:02:52.180
We'll go back to water
and sugar--

00:02:52.180 --> 00:02:54.070
especially back to water.

00:02:54.070 --> 00:02:58.570
Let's say we have a container
here and let's say it just has

00:02:58.570 --> 00:03:00.830
a bunch of-- let's say it just
has some air particles in it.

00:03:00.830 --> 00:03:03.560
It could be anything-- oxygen
or carbon dioxide.

00:03:03.560 --> 00:03:07.880
So let me just draw a couple
of air molecules here.

00:03:07.880 --> 00:03:11.060
So let's say that that is a
gaseous-- just for the sake of

00:03:11.060 --> 00:03:12.590
argument-- gaseous oxygen.

00:03:12.590 --> 00:03:14.900
So each of this is an O2--
each of those, right?

00:03:14.900 --> 00:03:16.900
And let's say that this is the
current configuration, that

00:03:16.900 --> 00:03:19.710
all of this is a vacuum here
and that there's some

00:03:19.710 --> 00:03:20.220
temperatures.

00:03:20.220 --> 00:03:22.490
So these water molecules,
they have some

00:03:22.490 --> 00:03:25.280
type of kinetic energy.

00:03:25.280 --> 00:03:29.620
They're moving in some type of
random directions right there.

00:03:29.620 --> 00:03:34.760
So my question is, what is going
to happen in this type

00:03:34.760 --> 00:03:35.810
of container?

00:03:35.810 --> 00:03:38.710
Well, any of these guys are
going to be randomly bumping

00:03:38.710 --> 00:03:39.770
into each other.

00:03:39.770 --> 00:03:43.030
They're more likely to bump into
things in this down-left

00:03:43.030 --> 00:03:45.120
direction than they are in
the up-right direction.

00:03:45.120 --> 00:03:47.970
So if this guy was happening
to go in this down-left

00:03:47.970 --> 00:03:50.110
direction, he's going to bump
into something and then

00:03:50.110 --> 00:03:52.070
ricochet into the up-right
direction.

00:03:52.070 --> 00:03:53.480
But in the up-right
direction, there's

00:03:53.480 --> 00:03:55.040
nothing to bounce into.

00:03:55.040 --> 00:03:57.990
So in general, everything is
moving in random directions,

00:03:57.990 --> 00:04:00.250
but you're more likely
to be able to move in

00:04:00.250 --> 00:04:01.000
the rightward direction.

00:04:01.000 --> 00:04:02.500
When you go to the left, you're
more likely to bump

00:04:02.500 --> 00:04:04.130
into something.

00:04:04.130 --> 00:04:06.090
So it's almost common sense.

00:04:06.090 --> 00:04:09.550
Over time, if you just let this
system come to some type

00:04:09.550 --> 00:04:11.580
of equilibrium-- I'm not
going to go into detail

00:04:11.580 --> 00:04:12.340
on what that means.

00:04:12.340 --> 00:04:14.340
You can watch the thermodynamics
videos if you'd

00:04:14.340 --> 00:04:15.470
like to see that.

00:04:15.470 --> 00:04:18.000
You'll eventually see the
container will look

00:04:18.000 --> 00:04:19.140
something like this.

00:04:19.140 --> 00:04:20.200
I can't guarantee it.

00:04:20.200 --> 00:04:22.500
There's some probability it
would actually stay like this,

00:04:22.500 --> 00:04:25.920
but very likely that those five
particles are going to

00:04:25.920 --> 00:04:27.970
get relatively spread out.

00:04:27.970 --> 00:04:32.790
This is diffusion and so it's
really just the spreading of

00:04:32.790 --> 00:04:36.940
particles or molecules from
high concentration to low

00:04:36.940 --> 00:04:39.140
concentration areas, right?

00:04:39.140 --> 00:04:41.420
In this case, the molecules are
going to spread in that

00:04:41.420 --> 00:04:43.780
direction from a high
concentration to a low

00:04:43.780 --> 00:04:45.130
concentration area.

00:04:45.130 --> 00:04:47.920
Now you're saying, Sal,
what is concentration?

00:04:47.920 --> 00:04:51.060
And there's many ways to measure
concentration and you

00:04:51.060 --> 00:04:54.120
can go into molarity and
molality and all of that.

00:04:54.120 --> 00:04:57.830
But the very simple idea is, how
much of that particle do

00:04:57.830 --> 00:04:59.900
you have per unit space?

00:04:59.900 --> 00:05:02.780
So here, you have a lot of those
particles per unit space

00:05:02.780 --> 00:05:04.550
and here you have very
few of those

00:05:04.550 --> 00:05:05.850
particles per unit space.

00:05:05.850 --> 00:05:09.230
So this is a high concentration
and that's a low

00:05:09.230 --> 00:05:09.970
concentration.

00:05:09.970 --> 00:05:12.740
So you could imagine other
experiments like this.

00:05:12.740 --> 00:05:17.000
You could imagine a solution
like-- let's do

00:05:17.000 --> 00:05:18.250
something like this.

00:05:21.570 --> 00:05:22.820
Let's say I have
two containers.

00:05:25.440 --> 00:05:27.230
Let's go back to the
solution situation.

00:05:27.230 --> 00:05:29.720
This was a gas, but I started
off with that example so let's

00:05:29.720 --> 00:05:31.432
stay with that example.

00:05:31.432 --> 00:05:35.530
So let's say that I have a door
right there that's larger

00:05:35.530 --> 00:05:38.370
than either the water or
the sugar molecules.

00:05:38.370 --> 00:05:41.305
On either side, I have a bunch
of water molecules.

00:05:52.020 --> 00:05:53.300
So I have a lot of
water molecules.

00:05:53.300 --> 00:05:55.650
So if I just had water molecules
here-- they're all

00:05:55.650 --> 00:05:58.690
bouncing around in random
directions-- and so the odds

00:05:58.690 --> 00:06:01.890
of a water molecule going this
way, equivalent to odds of a

00:06:01.890 --> 00:06:04.590
water molecule going that way,
assuming that both sides have

00:06:04.590 --> 00:06:06.570
the same level of water
molecule, otherwise the

00:06:06.570 --> 00:06:07.510
pressures would be different.

00:06:07.510 --> 00:06:10.070
But let's say that the top
of this is the same

00:06:10.070 --> 00:06:11.170
as the top of this.

00:06:11.170 --> 00:06:12.730
So there's no more pressure
going in one

00:06:12.730 --> 00:06:13.790
direction or another.

00:06:13.790 --> 00:06:17.240
So if for whatever reason, a
bunch more water molecules

00:06:17.240 --> 00:06:18.772
were going in the rightward
direction, then all of a

00:06:18.772 --> 00:06:20.760
sudden this would fill up with
more water and we know that

00:06:20.760 --> 00:06:22.620
that isn't likely to occur.

00:06:22.620 --> 00:06:28.200
So this is just two containers
of water.

00:06:28.200 --> 00:06:30.340
Now let's put some
solute in it.

00:06:30.340 --> 00:06:33.230
Let's dissolve some solute in it
and let's say we do all the

00:06:33.230 --> 00:06:35.630
dissolving on the
left-hand side.

00:06:35.630 --> 00:06:40.620
So we put some sugar molecules
on the left-hand side.

00:06:40.620 --> 00:06:42.910
And these are small enough to
fit through this little pipe.

00:06:42.910 --> 00:06:44.280
That's one assumption
that I'm making.

00:06:44.280 --> 00:06:45.120
So what's going to happen?

00:06:45.120 --> 00:06:47.710
All of these things have some
type of kinetic energy.

00:06:47.710 --> 00:06:52.630
They're all bouncing around.

00:06:52.630 --> 00:06:56.250
Well, over time, the water's
going back and forth.

00:06:56.250 --> 00:06:57.600
This water molecule
might go that way.

00:06:57.600 --> 00:07:00.040
That water molecule might go
that way, but they net each

00:07:00.040 --> 00:07:03.810
other out, but over time one of
these big sugar molecules

00:07:03.810 --> 00:07:06.520
will be going in just the
right direction to go

00:07:06.520 --> 00:07:08.470
through-- maybe this guy's,
instead of going that

00:07:08.470 --> 00:07:10.380
direction, he starts off going
in that direction.

00:07:10.380 --> 00:07:15.630
He goes just through this tunnel
connecting the two

00:07:15.630 --> 00:07:18.050
containers and he'll end
up there, right?

00:07:18.050 --> 00:07:20.320
And this guy will still
be bouncing around.

00:07:20.320 --> 00:07:23.570
There's some probability he goes
back, but there's still

00:07:23.570 --> 00:07:25.420
more sugar particles
here than there.

00:07:25.420 --> 00:07:31.350
So there's still more
probability that one of these

00:07:31.350 --> 00:07:33.350
guys will go to that side
than one of these guys

00:07:33.350 --> 00:07:34.340
will go to that side.

00:07:34.340 --> 00:07:36.980
So you can imagine if you're
doing this with gazillions of

00:07:36.980 --> 00:07:40.650
particles-- I'm only doing it
with four-- over time, the

00:07:40.650 --> 00:07:43.440
particles will have spread out
so that their concentrations

00:07:43.440 --> 00:07:44.550
are roughly equal.

00:07:44.550 --> 00:07:46.950
So that maybe you'll have
two here over time.

00:07:46.950 --> 00:07:49.430
But when you're only dealing
with three or four or five

00:07:49.430 --> 00:07:51.380
particles, there's some
probability it doesn't happen,

00:07:51.380 --> 00:07:53.240
but when you're doing it with a
gazillion and they're super

00:07:53.240 --> 00:07:56.810
small, it's a very, very,
very high likelihood.

00:07:56.810 --> 00:07:59.590
But anyway, this whole process--
we went from a

00:07:59.590 --> 00:08:02.460
container of high concentration
to a container

00:08:02.460 --> 00:08:06.080
of low concentration and the
particles would have spread

00:08:06.080 --> 00:08:08.530
from the low concentration
container to the high

00:08:08.530 --> 00:08:09.590
concentration container.

00:08:09.590 --> 00:08:11.130
So they diffused.

00:08:11.130 --> 00:08:12.820
This is diffusion.

00:08:16.170 --> 00:08:18.880
And just so that we learn some
other words that tend to be

00:08:18.880 --> 00:08:21.800
used with the idea of
diffusion-- when we started

00:08:21.800 --> 00:08:24.260
off, this had a higher
concentration.

00:08:24.260 --> 00:08:26.715
The left-hand side container
had higher concentration.

00:08:33.110 --> 00:08:34.130
It's all relative, right?

00:08:34.130 --> 00:08:37.480
It's higher than this guy.

00:08:37.480 --> 00:08:39.505
And this right here had
a lower concentration.

00:08:42.799 --> 00:08:44.450
And there are words
for these things.

00:08:44.450 --> 00:08:47.650
This solution with a high
concentration is called a

00:08:47.650 --> 00:08:50.330
hypertonic solution.

00:08:50.330 --> 00:08:51.730
Let me write that in yellow.

00:08:58.330 --> 00:09:01.120
Hyper, in general, meaning
having a lot of something,

00:09:01.120 --> 00:09:02.620
having too much of something.

00:09:02.620 --> 00:09:05.925
And this lower concentration
is hypotonic.

00:09:13.720 --> 00:09:16.660
You might have heard maybe one
of your relatives, if they

00:09:16.660 --> 00:09:20.730
haven't had a meal in awhile
say, I'm hypoglycemic.

00:09:20.730 --> 00:09:22.230
That means that they have
not-- they're feeling

00:09:22.230 --> 00:09:22.910
lightheaded.

00:09:22.910 --> 00:09:24.800
There's not enough sugar in
their bloodstream and they

00:09:24.800 --> 00:09:26.730
want to pass out so
they want a meal.

00:09:26.730 --> 00:09:29.930
If you just had a candy bar,
maybe you're hyperglycemic--

00:09:29.930 --> 00:09:32.930
or maybe you're just
hyper in general.

00:09:32.930 --> 00:09:35.580
So these are just good
prefixes to know, but

00:09:35.580 --> 00:09:38.650
hypertonic-- you have
a lot of the solute.

00:09:38.650 --> 00:09:40.510
You have a high concentration.

00:09:40.510 --> 00:09:44.500
And then in hypotonic, not too
much of the solute so you have

00:09:44.500 --> 00:09:46.010
a low concentration.

00:09:46.010 --> 00:09:47.130
These are good words to know.

00:09:47.130 --> 00:09:51.220
So in general, diffusion-- if
there's no barriers to the

00:09:51.220 --> 00:09:54.790
diffusion like we had here, you
will have the solute go

00:09:54.790 --> 00:09:58.820
from a high concentration or
hypertonic solution if they

00:09:58.820 --> 00:10:03.490
can travel to a hypotonic
solution, to a hypo, where the

00:10:03.490 --> 00:10:05.520
concentration is lower.

00:10:05.520 --> 00:10:08.480
Now let's do an interesting
experiment here.

00:10:08.480 --> 00:10:10.930
We've talked about diffusion and
so far we've been talking

00:10:10.930 --> 00:10:14.530
about the diffusion of
the solute, right?

00:10:14.530 --> 00:10:17.770
And in general-- and this is not
always the case-- if you

00:10:17.770 --> 00:10:19.780
want to be as general as
possible, the solute is

00:10:19.780 --> 00:10:22.400
whatever you have less of,
the solvent is whatever

00:10:22.400 --> 00:10:23.510
you have more of.

00:10:23.510 --> 00:10:26.600
And the most common solvent
tends to be water, but it

00:10:26.600 --> 00:10:27.520
doesn't have to be water.

00:10:27.520 --> 00:10:28.870
It could be some type
of alcohol.

00:10:28.870 --> 00:10:31.390
It could be mercury.

00:10:31.390 --> 00:10:34.880
It could be a whole set of
molecules, but water in most

00:10:34.880 --> 00:10:38.130
biological or chemical systems
tends to be the

00:10:38.130 --> 00:10:39.460
most typical solvent.

00:10:39.460 --> 00:10:41.920
It's what other things
are dissolved into.

00:10:41.920 --> 00:10:46.380
But what happens if we have a
tunnel where the solute is too

00:10:46.380 --> 00:10:51.060
big to travel, but water is
small enough to travel?

00:10:51.060 --> 00:10:55.370
Let's think about
that situation.

00:10:55.370 --> 00:10:57.090
In order to think about it,
I'm going to do something

00:10:57.090 --> 00:10:58.830
interesting.

00:10:58.830 --> 00:11:02.670
Let's say we have a
container here.

00:11:02.670 --> 00:11:03.950
Actually, I won't even
draw a container.

00:11:03.950 --> 00:11:07.190
Let's just say we have an
outside environment that has a

00:11:07.190 --> 00:11:09.260
bunch of water.

00:11:09.260 --> 00:11:12.630
This is the outside environment
and then you have

00:11:12.630 --> 00:11:13.880
some type of membrane.

00:11:19.400 --> 00:11:22.040
Water can go in and out
of this membrane.

00:11:22.040 --> 00:11:23.190
So it's semi-permeable.

00:11:23.190 --> 00:11:26.520
Well, it's permeable to water,
but the solute cannot go

00:11:26.520 --> 00:11:27.110
through the membrane.

00:11:27.110 --> 00:11:28.680
So let's say that the
solute is sugar.

00:11:28.680 --> 00:11:33.060
So we have water on
the outside and

00:11:33.060 --> 00:11:36.126
also inside the membrane.

00:11:36.126 --> 00:11:39.380
So these are little small
water molecules.

00:11:39.380 --> 00:11:43.950
This is a membrane right here.

00:11:43.950 --> 00:11:46.520
And let's say that we have some
sugar molecules again--

00:11:46.520 --> 00:11:47.560
I'm just picking on sugar.

00:11:47.560 --> 00:11:48.760
It could have been anything.

00:11:48.760 --> 00:11:51.050
So we have some sugar molecules
here that are just a

00:11:51.050 --> 00:11:55.950
little bit bigger-- or they
could be a lot bigger.

00:11:55.950 --> 00:11:57.750
Actually, they're a lot bigger
than water molecules.

00:11:57.750 --> 00:11:59.700
You have a bunch of-- and I only
draw four, but you have a

00:11:59.700 --> 00:12:01.210
gazillion of them, right?

00:12:01.210 --> 00:12:03.470
You have that much more
water molecules.

00:12:03.470 --> 00:12:05.325
I'm just trying to show you have
more water molecules than

00:12:05.325 --> 00:12:06.290
sugar molecules.

00:12:06.290 --> 00:12:07.645
And this membrane is
semi-permeable.

00:12:13.140 --> 00:12:15.210
Permeable means it allows
things to pass.

00:12:15.210 --> 00:12:18.070
Semi-permeables means it's
not completely permeable.

00:12:18.070 --> 00:12:20.650
So semi-permeable-- in this
context, I'm saying I allow

00:12:20.650 --> 00:12:22.440
water to pass through
the membrane.

00:12:22.440 --> 00:12:28.850
So water can pass,
but sugar cannot.

00:12:28.850 --> 00:12:30.100
Sugar is too large.

00:12:35.900 --> 00:12:39.220
So if we were to zoom in on the
actual membrane itself--

00:12:39.220 --> 00:12:40.580
maybe the membrane
looks like this.

00:12:40.580 --> 00:12:41.980
I'm going to zoom in
on this membrane.

00:12:44.530 --> 00:12:48.620
So it has little holes in the
membrane, just like that.

00:12:48.620 --> 00:12:51.270
And maybe the water molecules
are about that size.

00:12:51.270 --> 00:12:53.820
So they can go through
those holes.

00:12:53.820 --> 00:12:56.250
So the water molecules can go
back and forth through the

00:12:56.250 --> 00:13:01.520
holes, but the sugar molecules
are about that big.

00:13:01.520 --> 00:13:04.990
So they cannot go through
that hole.

00:13:04.990 --> 00:13:07.280
They're too big for this opening
right here to go back

00:13:07.280 --> 00:13:08.830
and forth between them.

00:13:08.830 --> 00:13:12.680
Now what do you think is going
to happen in this situation?

00:13:12.680 --> 00:13:14.330
So first of all, let's
use our terminology.

00:13:14.330 --> 00:13:15.720
Remember, sugar is our solute.

00:13:15.720 --> 00:13:17.120
Water is our solvent.

00:13:17.120 --> 00:13:18.930
Semi-permeable membrane.

00:13:18.930 --> 00:13:21.400
Which side of the membrane
has a higher or lower

00:13:21.400 --> 00:13:24.330
concentration of solute?

00:13:24.330 --> 00:13:25.690
Well, the inside does.

00:13:25.690 --> 00:13:27.060
The inside is hypertonic.

00:13:32.370 --> 00:13:33.540
The outside has a lower

00:13:33.540 --> 00:13:34.850
concentration so it's hypotonic.

00:13:44.850 --> 00:13:47.680
Now, if these openings were big
enough, based on what we

00:13:47.680 --> 00:13:51.330
just talked about-- these guys
are bouncing around, water is

00:13:51.330 --> 00:13:53.700
travelling in either direction,
and equal

00:13:53.700 --> 00:13:56.520
probability or-- actually
I'm going to talk

00:13:56.520 --> 00:13:58.360
about that in a second.

00:13:58.360 --> 00:14:01.660
If everything was wide open, it
would be equal probability,

00:14:01.660 --> 00:14:03.780
but if it was wide open, these
guys eventually would bounce

00:14:03.780 --> 00:14:06.450
their ways over to this side and
you'd probably end up with

00:14:06.450 --> 00:14:08.500
equal concentrations
eventually.

00:14:08.500 --> 00:14:10.710
And so you would have your
traditional diffusion, where

00:14:10.710 --> 00:14:13.130
high concentration
of solute to low

00:14:13.130 --> 00:14:14.530
concentrations of solute.

00:14:14.530 --> 00:14:17.350
But in this case, these
guys-- they can't

00:14:17.350 --> 00:14:18.330
fit through the hole.

00:14:18.330 --> 00:14:20.160
Only water can go
back and forth.

00:14:20.160 --> 00:14:25.180
If these guys were not here,
water would have an equal

00:14:25.180 --> 00:14:28.780
likelihood of going in this
direction as they would be

00:14:28.780 --> 00:14:33.940
going in that direction, a
completely equal likelihood.

00:14:33.940 --> 00:14:40.090
But because these guys are on
the right-hand side of-- or in

00:14:40.090 --> 00:14:42.290
this case, on the inside
of our membrane.

00:14:42.290 --> 00:14:47.000
This is our inside of our
membrane zoomed up-- it's less

00:14:47.000 --> 00:14:50.440
likely because these guys
might be in the approach

00:14:50.440 --> 00:14:55.230
position of the holes-- that's
slightly less likely for water

00:14:55.230 --> 00:14:58.110
to be in the approach position
for the holes so it's actually

00:14:58.110 --> 00:15:02.720
more probable that water could
enter than water exit.

00:15:02.720 --> 00:15:04.180
And I want to make
that very clear.

00:15:04.180 --> 00:15:07.150
If these sugar molecules were
not here, obviously it's

00:15:07.150 --> 00:15:09.830
equally likely for water to
go in either direction.

00:15:09.830 --> 00:15:12.730
Now that these sugar molecules
are there, these sugar

00:15:12.730 --> 00:15:15.290
molecules might be on
the right-hand side.

00:15:15.290 --> 00:15:18.200
They might be blocking-- I guess
the best way to think

00:15:18.200 --> 00:15:20.430
about it is blocking the
approach to the hole.

00:15:20.430 --> 00:15:22.060
They'll never be able to go
through the hole themselves

00:15:22.060 --> 00:15:24.490
and might not even be blocking
the hole, but they're going in

00:15:24.490 --> 00:15:25.720
some random direction.

00:15:25.720 --> 00:15:29.580
So if a water molecule was
approaching-- it's all

00:15:29.580 --> 00:15:31.360
probabilistic and we're dealing
with gazillions of

00:15:31.360 --> 00:15:34.610
molecules-- it's that much more
likely to be blocked to

00:15:34.610 --> 00:15:35.360
get outside.

00:15:35.360 --> 00:15:37.620
But the water molecules from the
outside-- there's nothing

00:15:37.620 --> 00:15:40.170
blocking them to get in so
you're going to have a flow of

00:15:40.170 --> 00:15:41.480
water inside.

00:15:41.480 --> 00:15:44.310
So in this situation, with a
semi-permeable membrane,

00:15:44.310 --> 00:15:45.700
you're going to have water.

00:15:45.700 --> 00:15:49.280
You're going to have a net
inward flow of water.

00:15:49.280 --> 00:15:51.430
And so this is kind
of interesting.

00:15:51.430 --> 00:15:56.900
We have the solvent flowing from
a hypotonic situation to

00:15:56.900 --> 00:15:59.600
a hypertonic solution,
but it's only

00:15:59.600 --> 00:16:01.210
hypotonic in the solute.

00:16:07.650 --> 00:16:11.620
But water-- if you flip it the
other way-- if you've used

00:16:11.620 --> 00:16:15.290
sugar as the solvent, then you
could say, we're going from a

00:16:15.290 --> 00:16:19.470
high concentration of water to
a low concentration of water.

00:16:19.470 --> 00:16:20.370
I don't want to confuse
you too much.

00:16:20.370 --> 00:16:23.090
This is what tends to confuse
people, but just think about

00:16:23.090 --> 00:16:24.040
what's going to happen.

00:16:24.040 --> 00:16:27.260
No matter in what situation,
the solution is going to do

00:16:27.260 --> 00:16:30.000
what it can to try to
equilibriate the

00:16:30.000 --> 00:16:30.680
concentration.

00:16:30.680 --> 00:16:32.080
To make the concentrations
on both

00:16:32.080 --> 00:16:33.710
sides as close as possible.

00:16:33.710 --> 00:16:35.150
And it's not just some magic.

00:16:35.150 --> 00:16:36.160
It's not like the
solution knows.

00:16:36.160 --> 00:16:38.300
It's all based on probabilities
and these things

00:16:38.300 --> 00:16:41.050
bumping around, but in this
situation, water is more

00:16:41.050 --> 00:16:43.790
likely to flow into
the container.

00:16:43.790 --> 00:16:46.700
So it's actually going to go
from the hypotonic side when

00:16:46.700 --> 00:16:50.460
we talk about low concentration
of solute to the

00:16:50.460 --> 00:16:53.690
side that has high
concentrations of solute, of

00:16:53.690 --> 00:16:57.320
sugar-- and actually, if this
thing is stretchable, more

00:16:57.320 --> 00:17:01.670
water will keep flowing
in and this membrane

00:17:01.670 --> 00:17:04.420
will stretch out.

00:17:04.420 --> 00:17:08.420
I won't go to too much detail
here, but this idea of water--

00:17:08.420 --> 00:17:12.470
of the solvent-- if in this
case, water is the solvent--

00:17:12.470 --> 00:17:15.150
of water as a solvent
diffusing through a

00:17:15.150 --> 00:17:18.500
semi-permeable membrane,
this is called osmosis.

00:17:22.569 --> 00:17:25.170
You've probably heard learning
by osmosis-- if you put a book

00:17:25.170 --> 00:17:27.200
against your head, maybe it'll
just seep into your brain.

00:17:27.200 --> 00:17:28.000
Same idea.

00:17:28.000 --> 00:17:29.500
That's where the word
comes from.

00:17:29.500 --> 00:17:33.570
This idea of water seeping
through membranes to try to

00:17:33.570 --> 00:17:35.600
make concentrations
more equal.

00:17:35.600 --> 00:17:38.370
So if you say, well, I have high
concentration here, low

00:17:38.370 --> 00:17:39.490
concentration here.

00:17:39.490 --> 00:17:43.020
If there was no membrane here,
these big molecules would

00:17:43.020 --> 00:17:48.080
exit, but because there's this
semi-permeable membrane here,

00:17:48.080 --> 00:17:48.680
they can't.

00:17:48.680 --> 00:17:52.400
So the system just
probabilistically-- no magic

00:17:52.400 --> 00:17:56.090
here-- more water will enter
to try to equilibriate

00:17:56.090 --> 00:17:57.160
concentration.

00:17:57.160 --> 00:18:01.970
Eventually-- if maybe there's a
few molecules out here-- not

00:18:01.970 --> 00:18:06.440
as high concentration here--
eventually if everything was

00:18:06.440 --> 00:18:08.970
allowed to happen fully, you'll
get to the point where

00:18:08.970 --> 00:18:11.120
you have just as many--
you have just as high

00:18:11.120 --> 00:18:13.650
concentration on this side as
you have on the right-hand

00:18:13.650 --> 00:18:16.500
side because this right-hand
side is going to fill with

00:18:16.500 --> 00:18:19.380
water and also probably become
a larger volume.

00:18:19.380 --> 00:18:21.520
And then, once again, the
probabilities of a water

00:18:21.520 --> 00:18:23.600
molecule going to the right and
to the left will be the

00:18:23.600 --> 00:18:25.920
same and you'll get to some
type of equilibrium.

00:18:25.920 --> 00:18:29.910
But I want to make it very
clear-- diffusion is the idea

00:18:29.910 --> 00:18:33.130
of any particle going from
higher concentration and

00:18:33.130 --> 00:18:35.740
spreading into a region that has
a lower concentration and

00:18:35.740 --> 00:18:36.950
just spreading out.

00:18:36.950 --> 00:18:41.240
Osmosis is the diffusion
of water.

00:18:41.240 --> 00:18:44.210
And usually you're talking about
the diffusion of water

00:18:44.210 --> 00:18:47.010
as a solvent and usually it's
in the context of a

00:18:47.010 --> 00:18:51.260
semi-permeable membrane, where
the actual solute cannot

00:18:51.260 --> 00:18:53.530
travel through the membrane.

00:18:53.530 --> 00:18:55.800
Anyway, hopefully you've
found that useful and

00:18:55.800 --> 00:18:57.880
not completely confusing.


Parts of a cell

WEBVTT
Kind: captions
Language: en

00:00:00.400 --> 00:00:03.670
Let's talk a little bit about
the structure of the cell.

00:00:03.670 --> 00:00:06.480
I've done a lot of videos where
we deal with things that

00:00:06.480 --> 00:00:08.560
go on inside of them, but I
haven't done one where we just

00:00:08.560 --> 00:00:10.870
talk about the entire
structure of them.

00:00:10.870 --> 00:00:14.500
So a good place to start is--
let me just draw the membrane.

00:00:14.500 --> 00:00:17.850
And the cellular membrane is a
good place to start because

00:00:17.850 --> 00:00:20.780
this is what separates the cell
from the outside world,

00:00:20.780 --> 00:00:24.020
and to a large degree, it kind
of defines the cell.

00:00:24.020 --> 00:00:27.200
It defines it as this very,
very small compartment.

00:00:27.200 --> 00:00:29.220
That's where the word,
"cell" came from.

00:00:29.220 --> 00:00:30.870
So let me label that.

00:00:30.870 --> 00:00:35.390
Cellular membrane.

00:00:35.390 --> 00:00:39.570
And all cells have a
cellular membrane.

00:00:39.570 --> 00:00:45.490
Now if we think about maybe the
most important thing that

00:00:45.490 --> 00:00:48.590
defines a cell, you've probably
seen in the DNA

00:00:48.590 --> 00:00:50.680
videos and we're going to talk
about translation and

00:00:50.680 --> 00:00:53.300
transcription and all of that,
that what defines what a

00:00:53.300 --> 00:00:55.440
living organism is,
is its DNA.

00:00:55.440 --> 00:00:57.570
So all cells have DNA
inside of it.

00:00:57.570 --> 00:01:00.270
And I won't go into the details
of how DNA defines

00:01:00.270 --> 00:01:01.150
what an organism is.

00:01:01.150 --> 00:01:03.580
I've done that in some detail
on the DNA videos.

00:01:03.580 --> 00:01:05.019
But all cells have DNA.

00:01:05.019 --> 00:01:09.150
This is more of an anatomy of a
cell video than necessarily

00:01:09.150 --> 00:01:11.200
the function, but we'll go into
the function because we

00:01:11.200 --> 00:01:12.780
need to know what these
different parts do.

00:01:12.780 --> 00:01:16.610
So this is, right here,
this is the DNA.

00:01:16.610 --> 00:01:18.390
And it's in its chromatin
form here.

00:01:18.390 --> 00:01:21.190
There's also little
proteins here.

00:01:21.190 --> 00:01:23.170
Not in all organisms, but
we're going to stick to

00:01:23.170 --> 00:01:25.000
eukaryotes, and I'll talk
a little bit about the

00:01:25.000 --> 00:01:28.635
difference between eukaryotes
and prokaryotes in a second.

00:01:28.635 --> 00:01:29.940
But we have DNA.

00:01:29.940 --> 00:01:33.390
As I've drawn this cell right
now, this is pretty much any

00:01:33.390 --> 00:01:37.810
cell, and any animal or plant
or whatever kingdom

00:01:37.810 --> 00:01:38.840
could look like this.

00:01:38.840 --> 00:01:40.300
I haven't drawn a lot
of the details.

00:01:40.300 --> 00:01:43.270
I've just drawn the DNA and
the cellular membrane.

00:01:43.270 --> 00:01:47.460
Now here's kind of the first
major division in the living

00:01:47.460 --> 00:01:52.430
world, or at least from our
point of view, or it seemed

00:01:52.430 --> 00:01:54.560
obvious, is that some
cells have a

00:01:54.560 --> 00:01:58.330
membrane around the DNA.

00:01:58.330 --> 00:02:01.970
So they'll have a membrane
around the DNA that separates

00:02:01.970 --> 00:02:05.100
the DNA and the chromatin and
everything that makes up the

00:02:05.100 --> 00:02:08.090
stuff within the DNA, separates
that from the rest

00:02:08.090 --> 00:02:11.130
of the cell, and this
is called a nucleus.

00:02:11.130 --> 00:02:14.920
This is called a nucleus.

00:02:14.920 --> 00:02:17.670
And I said that's a major
division because when some

00:02:17.670 --> 00:02:19.770
people looked at some cells
and they saw a nucleus and

00:02:19.770 --> 00:02:21.780
other cells and they didn't see
a nucleus, they said, hey,

00:02:21.780 --> 00:02:25.210
this is a good way to classify
organisms. So they called the

00:02:25.210 --> 00:02:27.480
things that had nucleuses,
eukaryotes.

00:02:30.470 --> 00:02:32.150
These have a nucleus.

00:02:32.150 --> 00:02:36.950
So as I've drawn this cell right
here, it is a eukaryote.

00:02:36.950 --> 00:02:40.350
Now, if you do not have a
nucleus, you are dealing with

00:02:40.350 --> 00:02:41.600
a prokaryote.

00:02:44.180 --> 00:02:48.440
No nucleus.

00:02:48.440 --> 00:02:52.320
And examples of prokaryotes,
the two big groups of them,

00:02:52.320 --> 00:02:57.110
are bacteria and Archaea.

00:02:57.110 --> 00:02:58.200
Now, Archaea are really
interesting.

00:02:58.200 --> 00:03:00.900
We know very little
about them.

00:03:00.900 --> 00:03:04.190
They were originally thought to
be types of bacteria, but

00:03:04.190 --> 00:03:06.770
now people are realizing that
they're this whole completely

00:03:06.770 --> 00:03:10.870
other group, and we've actually
observed a very small

00:03:10.870 --> 00:03:13.050
subset of them, so it's a
very fascinating group.

00:03:13.050 --> 00:03:16.040
And it actually turns out that,
evolutionarily speaking,

00:03:16.040 --> 00:03:18.300
you shouldn't make this division
first. It actually

00:03:18.300 --> 00:03:21.800
makes more sense to divide
things into eukaryotes, I'll

00:03:21.800 --> 00:03:27.100
just write that Euk, bacteria
and Archaea.

00:03:27.100 --> 00:03:29.230
You don't want to do this
division first. There are

00:03:29.230 --> 00:03:31.370
actually three separate
groups that you want

00:03:31.370 --> 00:03:33.790
to start off with.

00:03:33.790 --> 00:03:35.840
We'll talk more about this
in future videos.

00:03:35.840 --> 00:03:37.280
But if you want to say
who has a nucleus?

00:03:37.280 --> 00:03:40.110
Well, eukaryotes have a
nucleus by definition.

00:03:40.110 --> 00:03:41.670
Who does not have a nucleus?

00:03:41.670 --> 00:03:46.110
Well, the bacteria and the
Archaea do not have nuclei,

00:03:46.110 --> 00:03:46.740
just like that.

00:03:46.740 --> 00:03:49.780
But I'm going to focus on
eukaryotes because they tend

00:03:49.780 --> 00:03:51.500
to be a little bit
more complex.

00:03:51.500 --> 00:03:53.070
They tend to be larger.

00:03:53.070 --> 00:03:55.720
And most of what we talk about,
at least in the videos

00:03:55.720 --> 00:03:57.810
so far, are dealing
with eukaryotes.

00:03:57.810 --> 00:04:02.840
Eukaryotes include plants,
animals-- we're animals, at

00:04:02.840 --> 00:04:08.680
least I am-- animals and fungi,
and there are other

00:04:08.680 --> 00:04:11.020
groups within eukaryotes, but
these are the ones that we

00:04:11.020 --> 00:04:14.290
normally deal with in
our everyday world.

00:04:14.290 --> 00:04:16.829
But let's go back to looking
at the anatomy of the cell.

00:04:16.829 --> 00:04:18.000
So we have our DNA.

00:04:18.000 --> 00:04:21.839
We know that it gets transcribed
into mRNA, That

00:04:21.839 --> 00:04:29.540
mRNA leaves the nucleus, and
it gets translated into

00:04:29.540 --> 00:04:32.390
proteins at the ribosomes.

00:04:32.390 --> 00:04:36.530
So the ribosomes are these
little complexes that could be

00:04:36.530 --> 00:04:38.780
floating all over the cell, and
we'll see in a second that

00:04:38.780 --> 00:04:41.430
they can also be attached
to these other membrane

00:04:41.430 --> 00:04:42.280
structures.

00:04:42.280 --> 00:04:43.530
So this is a ribosome.

00:04:47.560 --> 00:04:51.590
And if all this talk of DNA
transcription into mRNA and

00:04:51.590 --> 00:04:55.000
mRNA leaving the nucleus and
traveling to the ribosome to

00:04:55.000 --> 00:04:58.710
be translated into proteins
makes no sense to you, there

00:04:58.710 --> 00:05:00.720
are several videos where I
go into that in detail.

00:05:00.720 --> 00:05:02.660
But what I want to do is just
focus on all of the different

00:05:02.660 --> 00:05:04.820
parts to kind of give a
big picture of things.

00:05:04.820 --> 00:05:11.590
So ribosomes are where mRNA that
gets transcribed inside

00:05:11.590 --> 00:05:18.750
the nucleus from DNA, where it
gets translated into proteins.

00:05:18.750 --> 00:05:21.580
So you can kind of view them as
the place where information

00:05:21.580 --> 00:05:24.720
actually turns into proteins,
which then can be used

00:05:24.720 --> 00:05:27.500
anywhere else in the cell.

00:05:27.500 --> 00:05:30.160
And these ribosomes, they're
made up of proteins, and

00:05:30.160 --> 00:05:33.300
actually they're made up RNA.

00:05:33.300 --> 00:05:36.000
And so one question is, well,
where are the pieces of the

00:05:36.000 --> 00:05:37.080
ribosomes made?

00:05:37.080 --> 00:05:39.190
Well, some are made by proteins,
which might be made

00:05:39.190 --> 00:05:40.600
in other ribosomes.

00:05:40.600 --> 00:05:43.360
But some of it, the mRNA,
ribosomes, you can kind of

00:05:43.360 --> 00:05:46.770
view them as this big
mess, if you were to

00:05:46.770 --> 00:05:47.980
look at it in detail.

00:05:47.980 --> 00:05:49.900
There's some protein there.

00:05:49.900 --> 00:05:51.720
And I'm not drawing it that
realistically, but then you

00:05:51.720 --> 00:05:55.130
have some mRNA tied in with
the protein, and the mRNA

00:05:55.130 --> 00:05:58.490
isn't used for actual
information purposes like it

00:05:58.490 --> 00:06:01.060
normally is when it goes from
DNA to the ribosome.

00:06:01.060 --> 00:06:05.770
Within the ribosome itself,
ribosomal RNA is actually used

00:06:05.770 --> 00:06:06.890
as part of the structure.

00:06:06.890 --> 00:06:10.480
It actually helps the ribosome
function as a ribosome.

00:06:10.480 --> 00:06:12.420
So it's actually part
of the ribosome.

00:06:12.420 --> 00:06:20.060
And all of that gets built in
a part of the nucleus called

00:06:20.060 --> 00:06:22.960
the nucleolus or the nucleole.

00:06:22.960 --> 00:06:26.070
Let me write that down.

00:06:26.070 --> 00:06:28.970
So this right here, this is
interesting right here.

00:06:28.970 --> 00:06:34.680
This is the nucleolus
or the nucleole.

00:06:34.680 --> 00:06:36.860
And it isn't a separate
organelle, and it's not

00:06:36.860 --> 00:06:39.550
separated by a membrane, but it
shows up in a microscope.

00:06:39.550 --> 00:06:41.130
So when people first saw it,
they said, hey, there's like a

00:06:41.130 --> 00:06:41.980
bundle there.

00:06:41.980 --> 00:06:45.210
That must be like the core of
the nucleus or something.

00:06:45.210 --> 00:06:47.920
But it turns out what it is,
it's the densely packed--

00:06:47.920 --> 00:06:50.190
you've got DNA and RNA, and
that's actually where the

00:06:50.190 --> 00:06:54.240
ribosomal RNA, the stuff that
makes up the ribosomes, is

00:06:54.240 --> 00:06:55.020
actually produced.

00:06:55.020 --> 00:06:57.820
But it's so dense that it shows
up on a microscope, and

00:06:57.820 --> 00:07:00.080
that's why people decided to
name it something different.

00:07:00.080 --> 00:07:01.510
But it is not membrane bound.

00:07:01.510 --> 00:07:03.960
It's not an organelle
within an organelle.

00:07:03.960 --> 00:07:08.090
It's just densely packed
proteins and ribosomal RNA,

00:07:08.090 --> 00:07:11.550
and it's where ribosomal
RNA gets produced.

00:07:11.550 --> 00:07:13.620
So anyway, we're at
the ribosome.

00:07:13.620 --> 00:07:15.400
That's where proteins
get produced.

00:07:15.400 --> 00:07:18.030
But if the ribosomes are just
floating around, if they're

00:07:18.030 --> 00:07:21.340
free ribosomes, then those
proteins will just-- once

00:07:21.340 --> 00:07:23.430
they're produced at the
ribosome, they'll just float

00:07:23.430 --> 00:07:25.590
around here in the fluid
inside the cell

00:07:25.590 --> 00:07:26.840
that we call cytosol.

00:07:29.190 --> 00:07:32.830
But what if we wanted to produce
proteins that are

00:07:32.830 --> 00:07:36.950
supposed to end up, maybe in the
membrane of the cell, or

00:07:36.950 --> 00:07:39.850
maybe outside of the
cell itself?

00:07:39.850 --> 00:07:41.970
Cells produce things that are
used by other cells, that are

00:07:41.970 --> 00:07:43.450
used by the rest of the body.

00:07:43.450 --> 00:07:47.440
And here we have to go to
proteins that are attached to

00:07:47.440 --> 00:07:48.220
this membrane.

00:07:48.220 --> 00:07:50.580
You can kind of view it
as a bunch of tunnels.

00:07:50.580 --> 00:07:52.880
Let me see how well
I can draw that.

00:07:52.880 --> 00:07:55.130
I'm going to draw
it very roughly.

00:07:55.130 --> 00:07:58.670
You have this thing called the
endoplasmic reticulum.

00:07:58.670 --> 00:07:59.920
Endoplasmic reticulum.

00:08:01.990 --> 00:08:06.210
You can just view it as a bunch
of tunnels like that.

00:08:06.210 --> 00:08:07.460
Endoplasmic reticulum.

00:08:09.470 --> 00:08:13.140
And they eventually lead to
something called Golgi bodies,

00:08:13.140 --> 00:08:15.730
named after Mr. Golgi himself.

00:08:15.730 --> 00:08:18.110
So I'll do the endoplasmic
reticulum in yellow and I'll

00:08:18.110 --> 00:08:23.520
do the Golgi bodies in green
maybe, just like that.

00:08:23.520 --> 00:08:25.340
I'll tell you in a second
what they are.

00:08:25.340 --> 00:08:26.170
So what's going on?

00:08:26.170 --> 00:08:30.200
This is kind of a big kind of
stack, or you can kind of view

00:08:30.200 --> 00:08:32.250
it as a bunch of folded
membranes together.

00:08:32.250 --> 00:08:36.039
And some ribosomes are actually
attached to this

00:08:36.039 --> 00:08:38.840
part, which I call the
endoplasmic reticulum.

00:08:38.840 --> 00:08:42.880
So we have ribosomes attached.

00:08:42.880 --> 00:08:45.400
Some of them are free, some
of them are attached.

00:08:45.400 --> 00:08:47.060
And let me write
my labels down.

00:08:47.060 --> 00:08:51.540
So this right here, and we use
the space over here, this big

00:08:51.540 --> 00:08:55.430
flap of convoluted
membrane, that's

00:08:55.430 --> 00:08:56.680
the endoplasmic reticulum.

00:09:02.206 --> 00:09:04.020
It's fun to say.

00:09:04.020 --> 00:09:05.660
Endoplasmic reticulum.

00:09:05.660 --> 00:09:08.510
Maybe a good name for a band.

00:09:08.510 --> 00:09:11.780
Endoplasmic reticulum, and the
parts that have ribosomes

00:09:11.780 --> 00:09:14.860
attached to it are called the
rough endoplasmic reticulum.

00:09:14.860 --> 00:09:17.140
Maybe even a better
name for a band.

00:09:17.140 --> 00:09:21.750
So right here, where I have
attached ribosomes, so these

00:09:21.750 --> 00:09:24.770
ribosomes are attached right
here, this is the rough

00:09:24.770 --> 00:09:28.640
endoplasmic reticulum, or
maybe the rough ER.

00:09:28.640 --> 00:09:35.410
The rough ER, ER standing for
endoplasmic reticulum.

00:09:35.410 --> 00:09:38.210
And then where we don't have any
ribosomes attached, that's

00:09:38.210 --> 00:09:41.530
the smooth endoplasmic
reticulum.

00:09:41.530 --> 00:09:48.070
So right here, that is this
smooth endoplasmic reticulum.

00:09:48.070 --> 00:09:50.340
And I'm going to tell you in a
second what this is, but we

00:09:50.340 --> 00:09:51.870
can keep following
the membranes.

00:09:51.870 --> 00:09:53.490
Eventually we get the
Golgi bodies.

00:09:57.650 --> 00:09:59.500
And what happens is,
I gave you a hint.

00:09:59.500 --> 00:10:02.430
In our free ribosomes, mRNA gets
there, gets translated

00:10:02.430 --> 00:10:04.610
into proteins, and the proteins
then just float

00:10:04.610 --> 00:10:06.360
around in the cytosol.

00:10:06.360 --> 00:10:08.930
But what if we want proteins
that should end up in

00:10:08.930 --> 00:10:11.190
membranes or that end up
outside of the cell?

00:10:11.190 --> 00:10:14.000
And that's where the endoplasmic
reticulum and the

00:10:14.000 --> 00:10:15.890
Golgi bodies come into play.

00:10:15.890 --> 00:10:20.680
Because now what we can do is,
we have mRNA coming outside of

00:10:20.680 --> 00:10:24.560
the nucleus, and it can attach
to the ribosomes or it can be

00:10:24.560 --> 00:10:27.690
translated by the ribosomes
in the rough ER.

00:10:27.690 --> 00:10:30.190
And what happens here is your
mRNA comes here and it's

00:10:30.190 --> 00:10:32.240
getting-- and I drew that
arrow very small-- it's

00:10:32.240 --> 00:10:34.725
getting translated on the
outside of the endoplasmic

00:10:34.725 --> 00:10:38.940
reticulum, but as the protein
gets produced, it's getting

00:10:38.940 --> 00:10:42.660
pushed into the inside of the
endoplasmic reticulum.

00:10:42.660 --> 00:10:44.950
And when I say the inside of the
endoplasmic reticulum, I'm

00:10:44.950 --> 00:10:46.590
talking about this area.

00:10:46.590 --> 00:10:47.470
I'm coloring it in.

00:10:47.470 --> 00:10:51.030
This is the inside of the
endoplasmic reticulum.

00:10:51.030 --> 00:10:53.070
And so the proteins will
get pushed into

00:10:53.070 --> 00:10:54.440
the endoplasmic reticulum.

00:10:54.440 --> 00:10:57.400
The ones that are to be used
outside of the cytosol,

00:10:57.400 --> 00:10:59.400
outside of the cell or maybe
in the cell's membrane.

00:10:59.400 --> 00:11:01.350
So proteins will end up here.

00:11:01.350 --> 00:11:04.120
That's why those ribosomes are
on the membrane, because they

00:11:04.120 --> 00:11:06.315
can translate things that are
outside of the endoplasmic

00:11:06.315 --> 00:11:11.800
reticulum, but as the proteins
get produced, the amino acid

00:11:11.800 --> 00:11:13.430
chain ends up inside of it.

00:11:13.430 --> 00:11:16.630
Let me make a blow-up
of that because I

00:11:16.630 --> 00:11:18.930
think that'll be useful.

00:11:18.930 --> 00:11:23.430
So let me draw-- let's say this
is the membrane of the

00:11:23.430 --> 00:11:26.450
endoplasmic reticulum
and then you have

00:11:26.450 --> 00:11:29.080
ribosomes attached to it.

00:11:29.080 --> 00:11:32.900
Let's say that's a ribosome on
the endoplasmic reticulum.

00:11:32.900 --> 00:11:35.860
And is this is going to be the
rough endoplasmic reticulum.

00:11:35.860 --> 00:11:39.790
And what you can have is mRNA
coming into one side of it.

00:11:43.820 --> 00:11:46.860
mRNA can kind of come
in through here.

00:11:46.860 --> 00:11:48.050
Maybe it's going in
that direction.

00:11:48.050 --> 00:11:51.430
It's getting translated
into the proteins.

00:11:51.430 --> 00:11:54.810
But then the protein, as the
amino acid chain is built up,

00:11:54.810 --> 00:11:57.710
will pop out on this end
of the membrane.

00:11:57.710 --> 00:12:00.300
Remember, this is our membrane
of our endoplasmic reticulum.

00:12:00.300 --> 00:12:03.070
So even though the mRNA is on
the outside, because the

00:12:03.070 --> 00:12:05.710
ribosome is attached to
it, the protein can

00:12:05.710 --> 00:12:06.790
show up on the inside.

00:12:06.790 --> 00:12:09.510
So once the protein is built,
maybe then it folds all up,

00:12:09.510 --> 00:12:13.900
you know, a protein is just a
folded chain of amino acids,

00:12:13.900 --> 00:12:16.375
it can travel through the
endoplasmic reticulum.

00:12:16.375 --> 00:12:17.920
And it travels through it.

00:12:17.920 --> 00:12:21.140
It travels through the smooth
endoplasmic reticulum all the

00:12:21.140 --> 00:12:22.590
way until it gets to
the Golgi bodies.

00:12:22.590 --> 00:12:23.870
And all sorts of other
things happen.

00:12:23.870 --> 00:12:26.223
I'm oversimplifying things, but
I just want to give you a

00:12:26.223 --> 00:12:28.580
sense of what everything
in the cell does.

00:12:28.580 --> 00:12:31.390
And once the protein travels to
the Golgi bodies and they

00:12:31.390 --> 00:12:35.230
get ready for traveling outside
of the cell, or maybe

00:12:35.230 --> 00:12:38.710
traveling to the cell's
membrane, they'll actually bud

00:12:38.710 --> 00:12:39.770
out of the Golgi bodies.

00:12:39.770 --> 00:12:42.530
So let's say this same protein,
when it gets to the

00:12:42.530 --> 00:12:45.225
Golgi bodies-- remember it's
inside of the Golgi body, so

00:12:45.225 --> 00:12:48.800
let me draw the membrane of the
Golgi body right there.

00:12:48.800 --> 00:12:50.520
The protein might
end up there.

00:12:50.520 --> 00:12:52.830
It's just a big chain
of amino acids.

00:12:52.830 --> 00:12:54.880
And then it will bud out.

00:12:54.880 --> 00:12:56.780
So let's say it looks like that,
and then maybe the next

00:12:56.780 --> 00:12:59.630
step it will look
something like.

00:12:59.630 --> 00:13:00.880
It will look like that.

00:13:07.180 --> 00:13:09.310
And the very next step, you
could imagine, will look

00:13:09.310 --> 00:13:11.870
something like this, where
it's actually completely

00:13:11.870 --> 00:13:12.420
budded out.

00:13:12.420 --> 00:13:15.850
It's popped out a little
of the membrane of the

00:13:15.850 --> 00:13:18.070
Golgi body with it.

00:13:18.070 --> 00:13:20.010
So now the protein
is surrounded by

00:13:20.010 --> 00:13:22.760
its own little membrane.

00:13:22.760 --> 00:13:24.590
So let's think about
what happened.

00:13:24.590 --> 00:13:27.260
We had DNA transcribed
into mRNA.

00:13:27.260 --> 00:13:30.980
mRNA goes to a ribosome
that's attached to

00:13:30.980 --> 00:13:32.740
the endoplasmic reticulum.

00:13:32.740 --> 00:13:35.740
It is translated into a protein
that travels through

00:13:35.740 --> 00:13:37.320
the endoplasmic reticulum.

00:13:37.320 --> 00:13:39.150
First, the rough, where
all the ribosomes

00:13:39.150 --> 00:13:40.410
are, then this smooth.

00:13:40.410 --> 00:13:41.740
The smooth has other
functions.

00:13:41.740 --> 00:13:48.520
It also helps produce hormones
and other fatty compounds, but

00:13:48.520 --> 00:13:49.850
I won't go into detail there.

00:13:49.850 --> 00:13:50.940
But it just travels.

00:13:50.940 --> 00:13:53.070
It connects to the
Golgi bodies.

00:13:53.070 --> 00:13:56.480
Then the Golgi bodies, the
proteins can bud off and take

00:13:56.480 --> 00:13:58.340
a little bit of the
membrane with it.

00:13:58.340 --> 00:14:01.900
And this idea of something being
surrounded by a membrane

00:14:01.900 --> 00:14:04.400
and just traveling in the cell,
so maybe the protein now

00:14:04.400 --> 00:14:06.100
looks like this.

00:14:06.100 --> 00:14:06.930
I'm enlarging it.

00:14:06.930 --> 00:14:09.380
Maybe the protein is there and
then it took a little bit of

00:14:09.380 --> 00:14:12.200
the Golgi body membrane
with it.

00:14:12.200 --> 00:14:14.780
This is called a vesicle.

00:14:14.780 --> 00:14:17.750
And this right here, let's add
another one right here.

00:14:17.750 --> 00:14:19.980
I'm just doing that
to label it.

00:14:19.980 --> 00:14:23.160
That's called a vesicle.

00:14:23.160 --> 00:14:26.110
And a vesicle is really just
a very general term for

00:14:26.110 --> 00:14:30.280
anything, little small things,
mostly proteins, in the cell

00:14:30.280 --> 00:14:32.430
that are just floating around,
that are surrounded by their

00:14:32.430 --> 00:14:34.320
own little mini-membranes.

00:14:34.320 --> 00:14:36.780
And the reason why this
mini-membrane is useful is now

00:14:36.780 --> 00:14:39.430
this protein can now
float to the outer

00:14:39.430 --> 00:14:40.430
membrane of the cell.

00:14:40.430 --> 00:14:42.130
It can also float to other
parts of the cell.

00:14:42.130 --> 00:14:43.780
I'm doing a simplification.

00:14:43.780 --> 00:14:47.010
And then it can merge either
with the membrane of the cell,

00:14:47.010 --> 00:14:50.950
or it can use this membrane,
this little vesicle membrane

00:14:50.950 --> 00:14:54.240
it has, to facilitate it getting
out of the cell.

00:14:54.240 --> 00:14:56.810
You can imagine that it
eventually, you know this

00:14:56.810 --> 00:15:00.430
thing-- let's say this is the
outer membrane of the cell.

00:15:00.430 --> 00:15:02.470
And I'm doing a gross
oversimplification.

00:15:02.470 --> 00:15:04.230
I'm not even drawing
the bilipid layer.

00:15:04.230 --> 00:15:07.580
But just to have a visual
impression of what it might

00:15:07.580 --> 00:15:11.880
look like, that's the vesicle
there, the little protein

00:15:11.880 --> 00:15:14.680
inside of it, and it gets
closer and closer to the

00:15:14.680 --> 00:15:18.530
membrane, and then it can
merge with the membrane

00:15:18.530 --> 00:15:20.300
because it's made up
of the same stuff.

00:15:20.300 --> 00:15:24.060
It merges with the membrane,
your protein inside.

00:15:24.060 --> 00:15:26.250
I switched colors arbitrarily.

00:15:26.250 --> 00:15:28.140
But now, all of a sudden, once
it merges with the membrane,

00:15:28.140 --> 00:15:31.920
then the protein can exit the
actual cell, or maybe it can

00:15:31.920 --> 00:15:35.210
actually embed itself within
this membrane, within the

00:15:35.210 --> 00:15:39.200
outer cellular membrane, which
I drew very thin, but it has

00:15:39.200 --> 00:15:39.960
two layers to it.

00:15:39.960 --> 00:15:40.970
And we'll talk more
about that.

00:15:40.970 --> 00:15:44.130
And I could probably make
a whole video on it.

00:15:44.130 --> 00:15:47.970
So those are-- we've already
made pretty good progress on

00:15:47.970 --> 00:15:49.400
showing the anatomy
of the cell.

00:15:49.400 --> 00:15:52.360
There are a few other things
we can throw in there.

00:15:52.360 --> 00:15:58.860
There are things called
lysosomes, which exist in

00:15:58.860 --> 00:16:03.840
animal cells that contain
enzymes in them that help

00:16:03.840 --> 00:16:05.155
dissolve other things.

00:16:08.720 --> 00:16:12.050
So if a lysosome attaches to
something else and is able to

00:16:12.050 --> 00:16:14.950
spew its enzymes into it,
it usually kills it.

00:16:14.950 --> 00:16:16.140
It usually digests it.

00:16:16.140 --> 00:16:18.100
So that's what a
lysosome does.

00:16:18.100 --> 00:16:23.310
In plants, you have things
called lytic vacuoles, and

00:16:23.310 --> 00:16:25.600
those are really the same thing
as a lysosome in terms

00:16:25.600 --> 00:16:28.280
of their function in that
they're really big vesicles.

00:16:28.280 --> 00:16:31.590
In fact, in general, a vacuole
is just a big vesicle.

00:16:31.590 --> 00:16:36.630
It's just a general term for a
big membrane-bound organelle.

00:16:36.630 --> 00:16:38.430
Vacuole.

00:16:38.430 --> 00:16:40.280
And once again, what's
an organelle?

00:16:40.280 --> 00:16:42.000
Let me write down that word.

00:16:42.000 --> 00:16:44.730
Organelle.

00:16:44.730 --> 00:16:48.780
It's just a membrane-bound
subunit of a cell.

00:16:48.780 --> 00:16:51.430
Just like my liver is a subunit
of Sal and it's an

00:16:51.430 --> 00:16:55.480
organ, an organelle is
a subunit of a cell.

00:16:55.480 --> 00:16:59.020
So a vacuole is just a general
term for a membrane-bound

00:16:59.020 --> 00:17:02.290
organelle that stores stuff
inside of our cells.

00:17:05.079 --> 00:17:08.400
So a lytic vacuole would be a
vacuole in a plant cell that

00:17:08.400 --> 00:17:10.440
stores a bunch of enzymes, and
if it were attached to

00:17:10.440 --> 00:17:12.619
something else it would dissolve
it if it were able to

00:17:12.619 --> 00:17:16.069
spew its enzymes into
the other thing.

00:17:16.069 --> 00:17:19.050
Now, there's several organelles
that we've talked

00:17:19.050 --> 00:17:21.230
about within the context
of respiration and

00:17:21.230 --> 00:17:24.619
photosynthesis, and I go into
detail in those videos.

00:17:24.619 --> 00:17:28.390
But we have things called
mitochondria.

00:17:28.390 --> 00:17:30.070
Mitochondrion cells.

00:17:30.070 --> 00:17:33.610
And they have inner and outer
membranes, and this is where

00:17:33.610 --> 00:17:38.470
we produce our energy, where
sugars are turned into ATP.

00:17:38.470 --> 00:17:40.270
I've done detailed
videos on this.

00:17:40.270 --> 00:17:43.350
These actually contain their own
DNA, and they can actually

00:17:43.350 --> 00:17:50.070
reproduce on their own, which
makes people believe that they

00:17:50.070 --> 00:17:54.780
exist-- that their ancestors
once existed as independent

00:17:54.780 --> 00:17:59.910
prokaryotic organisms, that at
some point they just kind of

00:17:59.910 --> 00:18:03.715
stumbled upon the notion of,
hey, why don't I live inside

00:18:03.715 --> 00:18:06.650
of other organisms and kind
of live in symbiosis?

00:18:06.650 --> 00:18:11.020
So mitochondria, these are
organelles that at one time

00:18:11.020 --> 00:18:13.140
their ancestors might have been
independent prokaryotes.

00:18:17.390 --> 00:18:19.400
Mitochondria.

00:18:19.400 --> 00:18:22.810
That's where cellular
respiration takes part, and we

00:18:22.810 --> 00:18:23.750
go into detail on that.

00:18:23.750 --> 00:18:26.640
And then on the plant cells,
this is only in-- well,

00:18:26.640 --> 00:18:29.830
definitely not in animal cells--
you have chloroplasts,

00:18:29.830 --> 00:18:31.900
which are a subset of things
called plastids, but

00:18:31.900 --> 00:18:33.990
chloroplasts are the
most famous.

00:18:33.990 --> 00:18:37.130
Maybe I should do that in
especially green, green.

00:18:37.130 --> 00:18:38.320
So we have chloroplasts.

00:18:38.320 --> 00:18:39.980
And we know they have little
thylakoids in there.

00:18:39.980 --> 00:18:41.750
This is where photosynthesis
takes place.

00:18:41.750 --> 00:18:43.270
You have your grana
and all of that.

00:18:43.270 --> 00:18:45.840
And I do go into detail in the
photosynthesis videos, but

00:18:45.840 --> 00:18:46.280
it's good to know.

00:18:46.280 --> 00:18:48.680
These are other organelles.

00:18:48.680 --> 00:18:51.950
And just like mitochondria, they
have their own DNA and

00:18:51.950 --> 00:18:53.440
their own ribosomes.

00:18:53.440 --> 00:18:56.780
And so the belief is that they
were once independent

00:18:56.780 --> 00:19:01.210
prokaryotes that learned to live
in symbiosis inside of

00:19:01.210 --> 00:19:04.090
larger eukaryotic cells.

00:19:04.090 --> 00:19:06.360
So we're almost done, really,
with the structure cells.

00:19:06.360 --> 00:19:08.620
There's other things we
can throw on here.

00:19:08.620 --> 00:19:12.800
If we're dealing with plant
cells or non-animal cells,

00:19:12.800 --> 00:19:15.080
we'll have something called a
cell wall, which will give

00:19:15.080 --> 00:19:17.380
some strength to the
outer membrane.

00:19:17.380 --> 00:19:19.090
You can kind of view
it that way, or it

00:19:19.090 --> 00:19:21.680
gives it some rigidity.

00:19:21.680 --> 00:19:23.480
So you have things called cell
walls, although they're not

00:19:23.480 --> 00:19:25.430
necessarily completely rigid.

00:19:25.430 --> 00:19:27.460
You can almost view them as
balloons that provide just a

00:19:27.460 --> 00:19:29.330
little bit more rigidity.

00:19:29.330 --> 00:19:32.530
Things like wood actually have
double cell walls for really

00:19:32.530 --> 00:19:33.400
hard-core rigidity.

00:19:33.400 --> 00:19:37.160
So this is a cell wall.

00:19:37.160 --> 00:19:39.170
This is in non-animals.

00:19:39.170 --> 00:19:43.810
And in plants it's made out of
cellulose, not cellulite.

00:19:43.810 --> 00:19:44.710
That used to confuse me.

00:19:44.710 --> 00:19:47.840
So this gives extra rigidity
or form to

00:19:47.840 --> 00:19:49.510
the cellular membrane.

00:19:49.510 --> 00:19:53.710
And then to actually give the
cell its actual structure, you

00:19:53.710 --> 00:19:56.450
have these things called
microfilaments, or sometimes

00:19:56.450 --> 00:19:58.890
actin filaments, and these are
these little pipes that go

00:19:58.890 --> 00:20:00.170
throughout the cell.

00:20:00.170 --> 00:20:03.810
These actually help give the
cell its actual structure in

00:20:03.810 --> 00:20:05.880
three dimensions, and actually,
they can participate

00:20:05.880 --> 00:20:08.150
in things moving around within
the cell or even the cell

00:20:08.150 --> 00:20:09.910
moving around itself.

00:20:09.910 --> 00:20:11.780
And just to be complete and
make sure we're covering

00:20:11.780 --> 00:20:15.620
everything, if you watch the
mitosis and meiosis videos,

00:20:15.620 --> 00:20:18.800
you have these things
called centrioles.

00:20:18.800 --> 00:20:19.940
I go into detail there.

00:20:19.940 --> 00:20:24.660
Centrioles that are right
outside of the nucleus.

00:20:24.660 --> 00:20:28.150
Two centrioles that are at right
angles to each other

00:20:28.150 --> 00:20:32.080
make up a centrosome, and they
kind of coordinate the

00:20:32.080 --> 00:20:36.870
microtubules when we start
splitting the cells in mitosis

00:20:36.870 --> 00:20:37.760
and meiosis.

00:20:37.760 --> 00:20:38.710
I won't go into detail there.

00:20:38.710 --> 00:20:40.490
I've done many videos
on that as well.

00:20:40.490 --> 00:20:42.930
But so far, this is pretty much
everything you need to

00:20:42.930 --> 00:20:46.860
know-- or at least a first
overview-- of the

00:20:46.860 --> 00:20:48.070
structure of the cell.

00:20:48.070 --> 00:20:50.960
And in one video, we finally
got it all in one place.

00:20:50.960 --> 00:20:54.060
This is pretty much-- I haven't
delved into detail on

00:20:54.060 --> 00:20:57.170
everything-- on all of the
major pieces of the cell.

00:20:57.170 --> 00:21:00.820
So hopefully, you have a better
big-picture view of how

00:21:00.820 --> 00:21:03.560
things are organized
inside of it.


Rational inequalities 2

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.470
Let's tackle a slightly
harder problem than what

00:00:02.470 --> 00:00:03.640
we saw in the last video.

00:00:03.640 --> 00:00:11.550
I have here x minus 3
over x plus 4 is greater

00:00:11.550 --> 00:00:14.550
than or equal to 2.

00:00:14.550 --> 00:00:17.630
So the reason why this is
slightly harder is I now have

00:00:17.630 --> 00:00:19.690
a greater than or equal to.

00:00:19.690 --> 00:00:21.490
And the other thing that makes
it slightly harder is I don't

00:00:21.490 --> 00:00:24.330
just have a simple 0 here,
I actually have a 2 here.

00:00:24.330 --> 00:00:26.360
So I'm going to do this
problem the same way.

00:00:26.360 --> 00:00:27.240
I'm going to do it two ways.

00:00:27.240 --> 00:00:28.800
I'm going to do the same two
ways we did last time, but I'm

00:00:28.800 --> 00:00:32.170
going to reverse the order of
the two ways that I do it.

00:00:32.170 --> 00:00:34.180
So the first thing I can do,
I might be tempted-- let me

00:00:34.180 --> 00:00:37.770
multiply both sides of this
equation times x plus 4.

00:00:37.770 --> 00:00:40.120
And like we saw in the last
video we had to be very

00:00:40.120 --> 00:00:42.350
careful because we have
an inequality here.

00:00:42.350 --> 00:00:46.200
If x plus 4 is greater than
0 then we're going to keep

00:00:46.200 --> 00:00:47.050
the inequality the same.

00:00:47.050 --> 00:00:48.840
If it's less than 0
we're going to swap it.

00:00:48.840 --> 00:00:50.800
So let's look at those
two situations.

00:00:50.800 --> 00:00:53.600
So one situation is-- let
me make it right here.

00:00:53.600 --> 00:00:58.720
One situation is x plus
4 is greater then 0.

00:00:58.720 --> 00:01:01.650
And remember, it can ever be
equal to 0 because then this

00:01:01.650 --> 00:01:03.740
expression would be undefined.

00:01:03.740 --> 00:01:06.300
So let's explore x plus
4 is greater than 0.

00:01:06.300 --> 00:01:09.650
If we subtract 4 from both
sides of this equation this is

00:01:09.650 --> 00:01:12.610
equivalent to saying-- these
are equivalent statements.

00:01:12.610 --> 00:01:15.810
If we subtract 4 from
both sides that x is

00:01:15.810 --> 00:01:17.800
greater than minus 4.

00:01:17.800 --> 00:01:20.720
So if we assume that x is
greater than minus 4 then

00:01:20.720 --> 00:01:23.040
x plus 4 is going to
be greater than 0.

00:01:23.040 --> 00:01:25.425
And then when we multiply
both sides of this times

00:01:25.425 --> 00:01:28.430
x plus 4-- let's do that.

00:01:28.430 --> 00:01:31.660
x minus 3 over x plus 4.

00:01:31.660 --> 00:01:33.020
You have your 2.

00:01:33.020 --> 00:01:38.720
We're going to multiply both
sides of this times x plus 4.

00:01:38.720 --> 00:01:41.710
Since we're assuming x is
greater than minus 4 or that x

00:01:41.710 --> 00:01:44.690
plus 4 is greater than 0, we
don't have to switch

00:01:44.690 --> 00:01:46.010
the inequality sign.

00:01:46.010 --> 00:01:48.010
We're multiplying both
sides by a positive.

00:01:48.010 --> 00:01:50.300
So the inequality stays
the same as in our

00:01:50.300 --> 00:01:51.530
original problem.

00:01:51.530 --> 00:01:53.380
And the whole reason why we
did that is because this

00:01:53.380 --> 00:01:54.810
and this will cancel out.

00:01:54.810 --> 00:01:56.390
And then we have 2
times x plus 4.

00:01:56.390 --> 00:01:57.870
Let's see what we get.

00:01:57.870 --> 00:02:03.700
x minus 3 is greater than
or equal to 2 times x plus

00:02:03.700 --> 00:02:06.420
2 times 4, which is 8.

00:02:06.420 --> 00:02:08.120
And now what can we do?

00:02:08.120 --> 00:02:10.530
We can subtract x
from both sides.

00:02:10.530 --> 00:02:15.700
We get minus 3 is greater
than or equal to x plus 8.

00:02:15.700 --> 00:02:17.860
I just took x from 2x.

00:02:17.860 --> 00:02:20.900
And then we can subtract
8 from both sides.

00:02:20.900 --> 00:02:22.640
So you subtract 8
from both sides.

00:02:22.640 --> 00:02:27.150
You get minus 3 minus 8
is minus 11 is greater

00:02:27.150 --> 00:02:28.580
than or equal to x.

00:02:28.580 --> 00:02:31.130
And of course, then we subtract
an 8 so this guy disappears.

00:02:31.130 --> 00:02:35.720
So if we assume that x is
greater than minus 4, then

00:02:35.720 --> 00:02:41.610
x has to be less than
or equal to minus 11.

00:02:41.610 --> 00:02:47.100
Now that seems a little
bit nonsensical.

00:02:47.100 --> 00:02:50.300
In order for this statement to
be true, x has to be both

00:02:50.300 --> 00:02:56.150
greater than minus 4 and it has
to be less than minus 11.

00:02:56.150 --> 00:02:58.460
Anything greater than
minus 4 is going to be

00:02:58.460 --> 00:03:00.240
greater than minus 11.

00:03:00.240 --> 00:03:04.310
So there's no x that
satisfies this equation.

00:03:04.310 --> 00:03:08.230
So if we assume that x plus 4
is greater than 0, we just end

00:03:08.230 --> 00:03:10.080
up with a nonsensical solution.

00:03:10.080 --> 00:03:13.090
So we can actually
ignore that path.

00:03:13.090 --> 00:03:16.280
There's no situation in which x
plus 4 is going to be greater

00:03:16.280 --> 00:03:19.030
than 0 and we're going to
actually have a solution

00:03:19.030 --> 00:03:20.250
to this equation.

00:03:20.250 --> 00:03:23.840
So let's assume what happens
when x plus 4 is less than 0.

00:03:23.840 --> 00:03:25.850
I'll do it here.

00:03:25.850 --> 00:03:29.120
So what happens when x
plus 4 is less than 0?

00:03:29.120 --> 00:03:30.860
And once again, that's an
equivalent statement.

00:03:30.860 --> 00:03:33.580
If we subtract 4 from both
sides of this equation

00:03:33.580 --> 00:03:37.530
to saying that x is
less than minus 4.

00:03:37.530 --> 00:03:38.880
These are equivalent
statements.

00:03:38.880 --> 00:03:41.780
So if we assume that x is less
than minus 4, then when we

00:03:41.780 --> 00:03:48.090
multiply both sides of this
equation times x plus 4 and

00:03:48.090 --> 00:03:55.300
you're multiplying it by
x minus 3 over x plus 4.

00:03:55.300 --> 00:03:56.840
And you have your 2 and
you're multiplying

00:03:56.840 --> 00:03:59.860
that times x plus 4.

00:03:59.860 --> 00:04:02.320
Since we're taking the other
situation where x is less than

00:04:02.320 --> 00:04:05.945
minus 4, which makes this
expression negative-- since

00:04:05.945 --> 00:04:08.630
we're multiplying both sides of
the equation by a negative, we

00:04:08.630 --> 00:04:13.780
swap the inequality
just like that.

00:04:13.780 --> 00:04:14.960
And let's see what we get.

00:04:14.960 --> 00:04:16.550
This and this cancel out.

00:04:16.550 --> 00:04:22.170
And then we get x minus 3 is
less than or equal to 2 times

00:04:22.170 --> 00:04:27.190
x plus 2 times 4, which is 8.

00:04:27.190 --> 00:04:30.100
And we do the same algebra.

00:04:30.100 --> 00:04:32.080
Let's subtract x
from both sides.

00:04:32.080 --> 00:04:35.955
We get minus 3 is less than
or equal to x plus 8.

00:04:35.955 --> 00:04:41.410
If we subtract 8 from both
sides we get minus 11 is

00:04:41.410 --> 00:04:43.800
less than or equal to x.

00:04:47.640 --> 00:04:50.790
If we assume this is
negative, we get x has

00:04:50.790 --> 00:04:54.290
to be less than minus 4.

00:04:54.290 --> 00:04:57.800
If x is less than minus 4, in
order for this equation to

00:04:57.800 --> 00:05:03.160
hold up, x also has to be
greater than minus 11.

00:05:03.160 --> 00:05:05.130
And this is actually possible.

00:05:05.130 --> 00:05:08.440
You can have an x, so x has
to be-- we can rewrite

00:05:08.440 --> 00:05:10.480
this-- greater than
or equal to minus 11.

00:05:10.480 --> 00:05:12.230
I just swapped the two sides.

00:05:12.230 --> 00:05:16.970
And x has to be
less than minus 4.

00:05:16.970 --> 00:05:20.720
And there are x's that satisfy
these two constraints.

00:05:20.720 --> 00:05:22.980
There weren't x's that satisfy
these two constraints.

00:05:22.980 --> 00:05:25.330
Nothing satisfies both of
these, but there are things

00:05:25.330 --> 00:05:26.870
that satisfy both of these.

00:05:26.870 --> 00:05:28.630
For example, minus 5.

00:05:28.630 --> 00:05:29.910
Let's draw this on
the number line.

00:05:29.910 --> 00:05:33.590
Let's draw a solution
to this problem.

00:05:33.590 --> 00:05:35.320
Let me keep the problem there.

00:05:35.320 --> 00:05:39.820
If I draw a number line,
I want to switch colors.

00:05:39.820 --> 00:05:41.390
So we have minus 11.

00:05:41.390 --> 00:05:44.010
We can be greater than
or equal to minus 11.

00:05:44.010 --> 00:05:46.370
So this is minus 11.

00:05:46.370 --> 00:05:48.740
And then we have
minus 4 over here.

00:05:51.610 --> 00:05:53.240
Maybe 0 sitting over there.

00:05:53.240 --> 00:05:54.980
We have to be less
than minus 4.

00:05:54.980 --> 00:05:57.820
Remember, we can ever be equal
to minus 4 because that

00:05:57.820 --> 00:05:59.240
would make this undefined.

00:05:59.240 --> 00:06:01.390
So we have to be less than
minus 4, so we don't

00:06:01.390 --> 00:06:03.010
include minus 4.

00:06:03.010 --> 00:06:06.490
We're less than minus 4,
but we have to be greater

00:06:06.490 --> 00:06:08.670
than or equal to 11.

00:06:08.670 --> 00:06:11.730
So we can't go less than
11, but we include the 11

00:06:11.730 --> 00:06:13.630
because this is greater
than or equal to.

00:06:13.630 --> 00:06:17.820
So anything in this, where I've
shaded it in-- anything on this

00:06:17.820 --> 00:06:20.960
range will satisfy that
equation over there.

00:06:20.960 --> 00:06:21.920
Now let's do it the other way.

00:06:21.920 --> 00:06:24.460
Let's do it where we-- the
numerator and denominator

00:06:24.460 --> 00:06:25.830
both have to be
positive or negative.

00:06:25.830 --> 00:06:29.530
Let's see if we can do the
same problem that way.

00:06:29.530 --> 00:06:34.330
So let me rewrite it down
here, maybe in a new color.

00:06:34.330 --> 00:06:35.880
So the same problem.

00:06:35.880 --> 00:06:44.370
x minus 3 over x plus 4 is
greater than or equal to 2.

00:06:44.370 --> 00:06:46.410
Now, in order to do that
reasoning that I did in the

00:06:46.410 --> 00:06:48.330
first video, remember the first
video I said, well, it's a

00:06:48.330 --> 00:06:51.060
divided by b is greater than 0.

00:06:51.060 --> 00:06:53.470
Either both of these are
positive or both of

00:06:53.470 --> 00:06:54.520
these are negative.

00:06:54.520 --> 00:06:56.450
But this only worked when
we had a 0 over here.

00:06:56.450 --> 00:06:59.180
But we don't have a 0 here we
have a 2 so we can't at least

00:06:59.180 --> 00:07:01.120
immediately do that rationale.

00:07:01.120 --> 00:07:03.360
But maybe we can if we
subtract 2 from both

00:07:03.360 --> 00:07:04.650
sides of this equation.

00:07:04.650 --> 00:07:05.740
So let's do that.

00:07:05.740 --> 00:07:12.610
So you have x minus 3 over x
plus 4 minus 2 is greater

00:07:12.610 --> 00:07:14.330
than or equal to 0.

00:07:14.330 --> 00:07:16.420
Just subtract a 2
from both sides.

00:07:16.420 --> 00:07:19.510
I can add or subtract without
messing up the inequality.

00:07:19.510 --> 00:07:20.460
Never have to worry about that.

00:07:20.460 --> 00:07:22.630
It's only when you multiply
by negatives that you

00:07:22.630 --> 00:07:24.380
swap the inequality.

00:07:24.380 --> 00:07:25.120
And now, what is this?

00:07:25.120 --> 00:07:27.160
You know, this doesn't look
like a rational expression.

00:07:27.160 --> 00:07:29.100
But I can rewrite
minus 2, right?

00:07:29.100 --> 00:07:34.930
Minus 2 is the same thing
as minus 2 times x

00:07:34.930 --> 00:07:38.640
plus 4 over x plus 4.

00:07:38.640 --> 00:07:40.380
This is minus 2 times 1.

00:07:40.380 --> 00:07:41.640
This is the same thing.

00:07:41.640 --> 00:07:45.925
And this is the same
thing as minus 2x plus--

00:07:45.925 --> 00:07:47.540
let me be careful.

00:07:47.540 --> 00:07:54.020
This is the same thing as minus
2x minus 8 over x plus 4.

00:07:54.020 --> 00:07:59.680
This right here is the exact
same thing as minus 2.

00:07:59.680 --> 00:08:02.420
I just multiply it times
x plus 4 for x plus 4.

00:08:02.420 --> 00:08:05.300
Let's write it this way
because then we can add them.

00:08:05.300 --> 00:08:10.620
So if we write that way, so I
have x minus 3 over x plus 4.

00:08:10.620 --> 00:08:12.960
And I wrote it that way so I
have a common denominator.

00:08:12.960 --> 00:08:19.900
And then I have plus minus
2x minus 8 over x plus

00:08:19.900 --> 00:08:22.250
4 is greater than 0.

00:08:22.250 --> 00:08:23.255
I have a common denominator.

00:08:23.255 --> 00:08:25.690
That was my whole
point of doing this.

00:08:25.690 --> 00:08:29.590
And so I have a denominator of
x plus 4 and then when you add

00:08:29.590 --> 00:08:32.720
these two things you
get x minus 2x.

00:08:32.720 --> 00:08:34.340
That's a minus x.

00:08:34.340 --> 00:08:39.120
And then you have minus 3
minus 8-- that's minus

00:08:39.120 --> 00:08:42.410
11-- is greater than 0.

00:08:42.410 --> 00:08:46.050
So now I simplify the problem
into something like this.

00:08:46.050 --> 00:08:47.430
So there's two situations.

00:08:47.430 --> 00:08:49.710
Oh, let me be very careful.

00:08:49.710 --> 00:08:51.010
This was greater than or equal.

00:08:51.010 --> 00:08:53.900
This must be greater
than or equal.

00:08:53.900 --> 00:08:55.370
Don't want to lose that
little equal sign.

00:08:55.370 --> 00:08:57.190
That was the whole
point of this problem.

00:08:57.190 --> 00:09:01.370
So now I'm ready to
operate just like this.

00:09:01.370 --> 00:09:03.370
Actually, before I even
do this, let's get one

00:09:03.370 --> 00:09:04.430
thing out of the way.

00:09:04.430 --> 00:09:05.966
Let's be very clear.

00:09:05.966 --> 00:09:08.960
x can never be
equal to minus 4.

00:09:08.960 --> 00:09:11.930
Because if x is equal to minus
4, this whole statement-- that

00:09:11.930 --> 00:09:12.960
original problem is undefined.

00:09:12.960 --> 00:09:14.850
So let's just write that first.

00:09:14.850 --> 00:09:16.475
You know, we could have
written that from the get-go.

00:09:16.475 --> 00:09:19.460
x cannot be equal to minus
4, for any solution.

00:09:19.460 --> 00:09:22.370
That will make this
expression undefined.

00:09:22.370 --> 00:09:25.570
Now, we have this and we saw in
the first video and we saw

00:09:25.570 --> 00:09:28.030
right there that there's
two situations.

00:09:28.030 --> 00:09:30.600
Either both of these
are positive.

00:09:30.600 --> 00:09:36.070
So they're either both
positive, so minus x minus 11

00:09:36.070 --> 00:09:40.090
is greater than or equal to 0.

00:09:40.090 --> 00:09:41.560
This could be equal to 0.

00:09:41.560 --> 00:09:43.740
Actually, if this is equal
to 0, then this whole

00:09:43.740 --> 00:09:44.570
thing is going to be true.

00:09:44.570 --> 00:09:51.220
So either that is greater than
or equal to 0 and this right

00:09:51.220 --> 00:09:52.980
here is greater than 0.

00:09:52.980 --> 00:09:54.460
It can't be equal to 0.

00:09:54.460 --> 00:09:59.110
And x plus 4 is greater than 0.

00:09:59.110 --> 00:10:03.650
That's the situation where
both of them are positive.

00:10:03.650 --> 00:10:07.510
Or they're both going
to be less than 0.

00:10:07.510 --> 00:10:08.820
And I'm running out of space.

00:10:08.820 --> 00:10:15.480
Or minus x minus 11 is
less than or equal to 0.

00:10:15.480 --> 00:10:17.850
And-- I'll write and like that.

00:10:17.850 --> 00:10:20.780
And x plus 4 is less than 0.

00:10:20.780 --> 00:10:22.470
Remember, it can't
ever equal 0.

00:10:22.470 --> 00:10:25.130
So they're either both
positive or both negative.

00:10:25.130 --> 00:10:26.810
That's the only way they we're
going to get something.

00:10:26.810 --> 00:10:28.680
Well, the numerator can be
equal to 0 because this

00:10:28.680 --> 00:10:29.720
thing can equal 0.

00:10:29.720 --> 00:10:32.150
Or they're both positive to
get something positive.

00:10:32.150 --> 00:10:34.840
Or they're both negative, so
that when you divide a negative

00:10:34.840 --> 00:10:37.780
by a negative you still
get something positive.

00:10:37.780 --> 00:10:40.030
So let's look at these two
situations and see if we get

00:10:40.030 --> 00:10:42.540
any solutions that make sense.

00:10:42.540 --> 00:10:46.180
So right here, if we add x to
both sides of this equation we

00:10:46.180 --> 00:10:50.830
get minus 11 is greater
than or equal to x.

00:10:50.830 --> 00:10:53.200
Or another way you could
say it, is x is less than

00:10:53.200 --> 00:10:54.820
or equal to minus 11.

00:10:54.820 --> 00:10:57.080
I just swapped these two sides.

00:10:57.080 --> 00:11:00.500
And then here, if we add minus
4-- if we subtract 4 from

00:11:00.500 --> 00:11:07.510
both sides we get x is
greater than minus 4.

00:11:07.510 --> 00:11:08.750
But once again, this
makes no sense.

00:11:08.750 --> 00:11:10.300
There's no way that I
can have-- remember

00:11:10.300 --> 00:11:11.710
there's an and here.

00:11:11.710 --> 00:11:13.670
Both of these have to be true.

00:11:13.670 --> 00:11:16.160
There's no x that is
greater than minus 4

00:11:16.160 --> 00:11:17.740
and less than minus 11.

00:11:17.740 --> 00:11:21.630
So this right here,
there's no constraints.

00:11:21.630 --> 00:11:24.560
So both of these can never be--
both the numerator and the

00:11:24.560 --> 00:11:27.820
denominator can never both be
positive at the same time

00:11:27.820 --> 00:11:30.320
because in order for them both
to be positive you get an

00:11:30.320 --> 00:11:31.890
impossible constraint to fill.

00:11:31.890 --> 00:11:33.720
So let's look at the situation.

00:11:33.720 --> 00:11:36.840
The other situation is when
they are both negative.

00:11:36.840 --> 00:11:38.970
When both this numerator
and this denominator

00:11:38.970 --> 00:11:40.840
are both negative.

00:11:40.840 --> 00:11:43.040
Let me be clear.

00:11:43.040 --> 00:11:44.610
You can't make a statement
about these two not

00:11:44.610 --> 00:11:45.550
being positive.

00:11:45.550 --> 00:11:47.450
These two things can
ever be positive.

00:11:47.450 --> 00:11:50.390
Remember, because we had to get
the 0 here in order to use

00:11:50.390 --> 00:11:51.940
this logic to begin with.

00:11:51.940 --> 00:11:55.310
So the fact that when we tried
to figure out x's that would

00:11:55.310 --> 00:11:58.810
make both of these positive, we
got a nonsensical, impossible

00:11:58.810 --> 00:12:01.890
to fill constraint, tells me
that both this numerator and

00:12:01.890 --> 00:12:06.550
this denominator can never both
be positive for any given x.

00:12:06.550 --> 00:12:08.860
Now let's see if they
can both be negative.

00:12:08.860 --> 00:12:10.800
So for both of them to be
negative or the numerator

00:12:10.800 --> 00:12:12.410
could also be equal to 0.

00:12:12.410 --> 00:12:17.130
If we add x to both sides
of this we get minus 11 is

00:12:17.130 --> 00:12:19.890
less than or equal to x.

00:12:19.890 --> 00:12:23.560
Or we could say that x is
greater than or equal to minus

00:12:23.560 --> 00:12:25.280
11 just swapping around.

00:12:25.280 --> 00:12:27.390
Over here, if we subtract
4 from both sides we have

00:12:27.390 --> 00:12:31.250
x is less than minus 4.

00:12:31.250 --> 00:12:32.210
And-- and this is an and.

00:12:32.210 --> 00:12:35.430
So x has to be greater than or
equal to minus 11 or less than

00:12:35.430 --> 00:12:38.850
minus 4, which is exactly what
we came up in the last problem.

00:12:38.850 --> 00:12:41.660
I can draw the
number line again.

00:12:41.660 --> 00:12:44.720
We have to be greater than
or equal to minus 11.

00:12:44.720 --> 00:12:46.860
So that's minus 11 there.

00:12:46.860 --> 00:12:49.890
We could be equal to it or
greater than, but we have

00:12:49.890 --> 00:12:51.250
to be less than minus 4.

00:12:51.250 --> 00:12:52.860
So this is minus 4.

00:12:52.860 --> 00:12:55.380
We can't even be equal to minus
4, that'll make our denominator

00:12:55.380 --> 00:12:57.070
undefined or our whole
equation undefined.

00:12:57.070 --> 00:12:59.590
It will make our denominator 0.

00:12:59.590 --> 00:13:01.140
And so this is our
solution set.

00:13:01.140 --> 00:13:04.460
Anything right here that I've
shaded in, including minus 11,

00:13:04.460 --> 00:13:06.220
but not including minus 4.

00:13:06.220 --> 00:13:08.530
So if you could get this
problem I think you can handle

00:13:08.530 --> 00:13:13.270
pretty much any rational
equation problem.

00:13:13.270 --> 00:13:15.110
Hope you enjoyed that.