Answer
$x=\{ -11,3 \}$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the given inequality, $
|x+4|=7
,$ is equivalent to
\begin{array}{l}\require{cancel}
x+4=7
\\\text{ OR }\\
x+4=-7
.\end{array}
Solving each equation separately, then,
\begin{array}{l}\require{cancel}
x=7-4
\\\\
x=3
\\\text{ OR }\\
x+4=-7
\\\\
x=-7-4
\\\\
x=-11
.\end{array}
Hence, $
x=\{ -11,3 \}
.$
