Answer
$x=-8\text{ OR }x=8$
Work Step by Step
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation, $
|-4x|=32
,$ is equivalent to
\begin{array}{l}\require{cancel}
-4x=32
\\\\\text{OR}\\\\
-4x=-32
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
-4x=32
\\
\dfrac{-4x}{-4}=\dfrac{32}{-4}
\\
x=-8
\\\\\text{OR}\\\\
-4x=-32
\\
\dfrac{-4x}{-4}=\dfrac{-32}{-4}
\\
x=8
.\end{array}
Hence, $
x=-8\text{ OR }x=8
.$
