#### Answer

$x=\{ -22,8 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the definition of absolute value equality to solve the given equation, $
|h+7|=15
.$ Do checking of the solution/s.
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
h+7=15
\\\\\text{OR}\\\\
h+7=-15
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
h+7=15
\\\\
h=15-7
\\\\
h=8
\\\\\text{OR}\\\\
h+7=-15
\\\\
h=-15-7
\\\\
h=-22
.\end{array}
If $h=8,$ then
\begin{array}{l}\require{cancel}
|h+7|=15?
\\\\
|8+7|=15?
\\\\
|15|=15?
\\\\
15=15
\text{ (TRUE)}
.\end{array}
If $h=-22,$ then
\begin{array}{l}\require{cancel}
|h+7|=15?
\\\\
|-22+7|=15?
\\\\
|-15|=15?
\\\\
15=15
\text{ (TRUE)}
.\end{array}
Hence, $
x=\{ -22,8 \}
.$