# How do you solve and write the following in interval notation: -19<10-x<=-11?

Jun 14, 2016

$21 \le x < 29.$
Interval Form : $x \in \left[21 , 29\right) .$
Given that, $- 19 < 10 - x \le - 11.$
We add -10 in the inequality (ineql.) to get, $- 29 < - x \le - 21.$
Then, we multiply this ineql. by $- 1$, a negative number, causing reversal of the order, $29 > + x \ge 21 ,$,i.e., $21 \le x < 29.$
We can write this in Interval Form as $x \in \left[21 , 29\right) .$