#### Solved Examples and Worksheet for Solving One Step Inequalities

Q1Jimmy & Sunny have $12 each. Sunny spends$5 on jellybeans, while Jimmy spends less on jellybeans. Which of the inequalities describes the money m left with Jimmy?
A. m > 12
B. m > 7
C. m ≥ 12
D. m < 7

Step: 1
Out of $12, Sunny spends$5 while Jimmy spends less than $5. [From the problem.] Step: 2 Sunny has$7 left with him and Jimmy has more than $7. [Money left = money initially had - money spent.] Step: 3 So, the inequality for the money left with Jimmy is m > 7. [m is the money left with Jimmy.] Correct Answer is : m > 7 Q2Sheela had more than$87 in her savings account. She withdrew $59 from her savings account. Which of the following inequalities best suits the balance amount m, in her savings account? A. m ≤ 28 B. m < 28 C. m ≥ 28 D. m > 28 Step: 1 Sheela withdrew$59 from her savings account, which had more than $87. Step: 2 The balance amount in her savings bank account will be more than 87 - 59=$28.
Step: 3
The inequality for the balance amount m is m > 28.
Correct Answer is :   m > 28
Q3Andy delivers bread packets to more than 66 families living in Dugway each day. Which of the following inequalities best describes the situation?
A. b ≤ 66
B. b > 66
C. b < 66
D. b ≥ 66

Step: 1
Let b be the bread packets delivered to the families living in Dugway.
Step: 2
Bread packets b, that Andy delivers to families living in Dugway are more than 66.
Step: 3
The inequality is b > 66.
Correct Answer is :   b > 66
Q4Jeff bought a pair of Guess jeans, which cost less than $50. Which of the following inequalities best describes the situation when the cost price is represented by p? A. p ≤ 50 B. p < 50 C. p > 50 D. p ≥ 50 Step: 1 Jeff bought a Guess jeans that costs less than$50.
Step: 2
The inequality is p < 50.
Correct Answer is :   p < 50
Q5Which of the following is a solution for the inequality below?
10.7 + x > 4.5

A. - 8.2
B. - 7.2
C. - 5.7
D. - 9.2

Step: 1
10.7 + x > 4.5
[Given inequality.]
Step: 2
10.7 + x - 10.7 > 4.5 - 10.7
[Subtract 10.7 from each side.]
Step: 3
x > - 6.2
[Simplify.]
Step: 4
The solution for the inequality is, all real numbers greater than - 6.2.
Step: 5
From the choices, the solution greater than - 6.2 is - 5.7.
Correct Answer is :   - 5.7
Q6Which of the following is a solution for the inequality? - 3.7 + x < - 4.5

A. -0.7
B. 0.9
C. -0.9
D. 0.1

Step: 1
- 3.7 + x < - 4.5
[Original inequality.]
Step: 2
- 3.7 + x + 3.7 < - 4.5 + 3.7
Step: 3
x < -0.8
[Simplify.]
Step: 4
The solution for the inequality is, all real numbers less than -0.8.
Step: 5
Among the choices, the solution for the inequality is -0.9 .
Q7Which of these is a solution for the inequality below?
x + 3.5 ≥ 6.8

A. 3.1
B. 3.4
C. 3.0
D. 3.2

Step: 1
x + 3.5 ≥ 6.8
[Original inequality.]
Step: 2
x + 3.5 - 3.5 ≥ 6.8 - 3.5
[Subtract 3.5 from each side.]
Step: 3
x ≥ 3.3
[Simplify.]
Step: 4
The solution for the inequality is, all real numbers greater than or equal to 3.3.
Step: 5
From the choices, the solution for the inequality is 3.4.
Q8Which of the following is a solution for the inequality x + 8.5 ≤ 3.8?

A. -4.7
B. -4.4
C. -4.5
D. -4.3

Step: 1
x + 8.5 ≤ 3.8
[Original inequality.]
Step: 2
x + 8.5 - 8.5 ≤ 3.8 - 8.5
[Subtract 8.5 from each side.]
Step: 3
x ≤ -4.7
[Simplify.]
Step: 4
The solution for the inequality is, all real numbers less than or equal to -4.7.
Step: 5
From the choices, the solution for the inequality is -4.7.
Q9There were fewer than 10 students in an English class. Which of the following inequalities best describes the situation when the number of students is represented by s?
A. s ≥ 10
B. s < 10
C. s > 10
D. s ≤ 10

Step: 1
There were fewer than 10 students in an English class.
Step: 2
The number of students is represented by s.
Step: 3
The inequality is s < 10.
Correct Answer is :   s < 10
Q10Annie had less than $106 in her savings account. She withdrew$68 from her savings account. Which of the following inequalities best suits the balance amount m, in her savings account?
A. m ≤ 38
B. m > 38
C. m ≥ 38
D. m < 38

Step: 1
Annie withdrew $68 from her savings account, which had less than$106.
Step: 2
The balance amount in her savings bank account will be less than 106 - 68 = \$38.
Step: 3
The inequality for the balance amount m is m < 38.
Correct Answer is :   m < 38
Q11Which of the following is not a solution of the inequality, x - 7 ≤ 2?
A. 8
B. 9
C. 7
D. 10

Step: 1
x - 7 ≤ 2
[Original inequality.]
Step: 2
x - 7 + 7 ≤ 2 + 7
Step: 3
x ≤ 9
[Simplify.]
Step: 4
Any real number, which is less than or equal to 9, is a solution for the inequality.
Step: 5
From the choices, 10 is the number which is not a solution of the inequality.
[10 is greater than 9.]
Q12Choose a solution for the inequality, x - 2 ≥ 49.
A. 41
B. 49
C. 51
D. 46

Step: 1
x - 2 ≥ 49
[Original inequality.]
Step: 2
x - 2 + 2 ≥ 49 + 2
Step: 3
x ≥ 51
[Simplify.]
Step: 4
The solution for the inequality is, all real numbers greater than or equal to 51.
Step: 5
From the choice, 51 is the correct answer.
Q13Which of the following is a solution for the inequality x + 3 ≥ 4?
A. -1
B. -2
C. 0
D. 1

Step: 1
x + 3 ≥ 4
[Original inequality.]
Step: 2
x + 3 - 3 ≥ 4 - 3
[Subtract 3 from each side.]
Step: 3
x ≥ 1
[Simplify.]
Step: 4
All real numbers greater than or equal to 1.
Step: 5
From the choices, the number greater than or equal to 1 is 1.
Q14Which of the choices represents the solution for the inequality, 9x > 81?
A. x < 9
B. x > 9
C. x ≥ 9
D. x ≤ 9

Step: 1
9x > 81
[Original inequality.]
Step: 2
9x9 > 819
[Divide by 9 on both sides, according to division property, if c > 0 and a > b then ac > bc.]
Step: 3
x > 9
[Simplify.]
Correct Answer is :   x > 9
Q15Choose the correct mathematical expression for the verbal description.

M is less than 6 times the value of 15 the height, where the height is H

A. M < 15H
B. M < 6 (15H)
C. M = 6 (15H)
D. M > 6 (15H)

Step: 1
The value of 15 the height = 15H
Step: 2
6 times the value of 15 the height = 6(15H)
Step: 3
M is less than 6 times the value of 15 the height can be written as M < 6(15H)
Correct Answer is :   M < 6 (15H)
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