#### Answer

$w=\{ -22,38 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the definition of absolute value equality to solve the given equation, $
|w-8|=30
.$ 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}
w-8=30
\\\\\text{OR}\\\\
w-8=-30
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
w-8=30
\\\\
w=30+8
\\\\
w=38
\\\\\text{OR}\\\\
w-8=-30
\\\\
w=-30+8
\\\\
w=-22
.\end{array}
If $w=38,$ then
\begin{array}{l}\require{cancel}
|w-8|=30?
\\\\
|38-8|=30?
\\\\
|30|=30?
\\\\
30=30
\text{ (TRUE)}
.\end{array}
If $w=-22,$ then
\begin{array}{l}\require{cancel}
|w-8|=30?
\\\\
|-22-8|=30?
\\\\
|-30|=30?
\\\\
30=30
\text{ (TRUE)}
.\end{array}
Hence, $
w=\{ -22,38 \}
.$