Answer
$[-9,-\frac{9}{2}]$
Work Step by Step
$-1 \leq \frac{2x}{3}+5 \leq 2$
Using properties of inequality, add $-5$ to all parts,
$-1-5 \leq \frac{2x}{3}+5 -5 \leq 2 -5$
$-6 \leq \frac{2x}{3} \leq -3$
Multiply all parts by $3$.
$-6 \times 3 \leq \frac{2x}{3} \times 3 \leq -3 \times 3$
$-18 \leq 2x \leq -9$
Divide by $2$
$\frac{-18}{2}\leq\frac{2x}{2}\leq\frac{-9}{2}$
$-9 \leq x \leq \frac{-9}{2}$
In Interval Notation: $[-9,\frac{-9}{2}]$
