Answer
The correct solution is $ x\lt -17$ or $x\gt 9$.
Work Step by Step
The given inequality is
$\Rightarrow |x+4|\gt13$
Write a compound inequality.
$\Rightarrow x+4\lt -13$ or $x+4\gt 13$
Subtract $4$ from each side.
$\Rightarrow x+4-4\lt -13-4$ or $x+4-4\gt 13-4$
Simplify.
$\Rightarrow x\lt -17$ or $x\gt 9$
Hence, the correct solution is $ x\lt -17$ or $x\gt 9$.
