Question

solve for z.
-7 ≤ 2z - 3 ≤ 11
write your answer as a compound inequality with integers.

Explanation:

Step1: Add 3 to all parts

$-7 + 3 \leq 2z - 3 + 3 \leq 11 + 3$
$\implies -4 \leq 2z \leq 14$

Step2: Divide all parts by 2

$\frac{-4}{2} \leq \frac{2z}{2} \leq \frac{14}{2}$
$\implies -2 \leq z \leq 7$

Answer:

$-2 \leq z \leq 7$