Answer
$\left[ -8,5 \right]$
Work Step by Step
The trigonometric equation is
$\left| 2x+3 \right|\le 13$
For $2x+3\ge 0$
$\begin{align}
& 2x+3\le 13 \\
& 2x\le 13-3 \\
& 2x\le 10 \\
& x\le 5
\end{align}$
For $2x+3\le 0$
$\begin{align}
& -\left( 2x+3 \right)\le 13 \\
& -2x-3\le 13 \\
& -2x\le \left( 13+3 \right) \\
& x\ge -8
\end{align}$
So, the region is $-8\le x\le 5$.
