#### Answer

$x=\{ 7,-11 \}$

#### Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the given equation, $
|x+2|=9
,$ is equivalent to
\begin{array}{l}\require{cancel}
x+2=9 \text{ OR } x+2=-9
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x+2=9
\\\\
x=9-2
\\\\
x=7
\\\\\text{ OR }\\\\
x+2=-9
\\\\
x=-9-2
\\\\
x=-11
.\end{array}
Hence, the solutions are $
x=\{ 7,-11 \}
.$