#### Answer

$x=\left\{ -8,8 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|5x|-3=37
,$ isolate first the absolute value expression. Then use the definition of an absolute value equality.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
|5x|-3=37
\\\\
|5x|=37+3
\\\\
|5x|=40
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
5x=40
\\\\\text{OR}\\\\
5x=-40
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
5x=40
\\\\
x=\dfrac{40}{5}
\\\\
x=8
\\\\\text{OR}\\\\
5x=-40
\\\\
x=-\dfrac{40}{5}
\\\\
x=-8
.\end{array}
Hence, $
x=\left\{ -8,8 \right\}
.$