Answer
$x=\left\{ 0,20 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|2-0.2x|=2
,$ use the definition of absolute value equality. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
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}
2-0.2x=2
\\\\\text{OR}\\\\
2-0.2x=-2
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2-0.2x=2
\\\\
-0.2x=2-2
\\\\
-0.2x=0
\\\\
x=\dfrac{0}{-0.2}
\\\\
x=0
\\\\\text{OR}\\\\
2-0.2x=-2
\\\\
-0.2x=-2-2
\\\\
-0.2x=-4
\\\\
10(-0.2x)=10(-4)
\\\\
-2x=-40
\\\\
x=\dfrac{-40}{-2}
\\\\
x=20
.\end{array}
Hence, $
x=\left\{ 0,20 \right\}
.$
