Answer
$w=\{ -15,15 \}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
3|w|-8=37
,$ isolate first the absolute value expression. Then use the definition of an absolute value equality to solve for the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given expression is equivalent to
\begin{array}{l}\require{cancel}
3|w|-8=37
\\\\
3|w|=37+8
\\\\
3|w|=45
\\\\
|w|=\dfrac{45}{3}
\\\\
|w|=15
.\end{array}
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=15
\\\\\text{OR}\\\\
w=-15
.\end{array}
Hence, $
w=\{ -15,15 \}
.$
