Answer
$x=\{ -20,20 \}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the definition of absolute value equality to solve the given equation, $
|x|=20
.$ 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}
x=-20
\\\\\text{OR}\\\\
x=20
.\end{array}
If $x=-20,$ then
\begin{array}{l}\require{cancel}
|-20|=20
\\\\
20=20
\text{ (TRUE)}
.\end{array}
If $x=20,$ then
\begin{array}{l}\require{cancel}
|20|=20
\\\\
20=20
\text{ (TRUE)}
.\end{array}
Hence, $
x=\{ -20,20 \}
.$
