Answer
$[−9,5]$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | x+2\right |+9\leq16$
Subtract $9$ from both sides.
$\Rightarrow \left | x+2\right |+9-9\leq16-9$
Simplify.
$\Rightarrow \left | x+2\right |\leq7$
Rewrite the inequality without absolute value bars.
$\Rightarrow-7 \leq x+2\leq7$
Solve compound inequality.
Subtract $2$ from all three parts.
$\Rightarrow-7 -2\leq x+2-2\leq7-2$
Simplify.
$\Rightarrow-9\leq x\leq5$
The solution set $[−9,5]$.
