#### Answer

$\left[ -16,10 \right]$

#### Work Step by Step

Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a,$ then the given inequality, $
|x+3|\le13
,$ is equivalent to
\begin{array}{l}\require{cancel}
-13\le x+3\le13
.\end{array}
Using the properties of inequality, then
\begin{array}{l}\require{cancel}
-13-3\le x+3-3\le13-3
\\\\
-16\le x\le10
.\end{array}
Hence, the solution is the interval $
\left[ -16,10 \right]
.$