Answer
$x\lt -11$ or $x\gt 5$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow |x+3|\gt8$
Write a compound inequality.
$\Rightarrow x+3\lt -8$ or $x+3\gt 8$
Subtract $3$ from each side.
$\Rightarrow x+3-3\lt -8-3$ or $x+3-3\gt 8-3$
Simplify.
$\Rightarrow x\lt -11$ or $x\gt 5$
Hence, the solution is $x\lt -11$ or $x\gt 5$.
