#### Answer

$x=\{ -5,5 \}$

#### Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $
|4x|=20
,$ is equivalent to
\begin{array}{l}\require{cancel}
4x=20 \text{ OR } 4x=-20
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
4x=20
\\\\
x=\dfrac{20}{4}
\\\\
x=5
\\\\\text{ OR }\\\\
4x=-20
\\\\
x=-\dfrac{20}{4}
\\\\
x=-5
.\end{array}
Hence, the solutions are $
x=\{ -5,5 \}
.$