Answer
$x=\left\{ 2,18 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|5-0.5x|=4
,$ 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}
5-0.5x=4
\\\\\text{OR}\\\\
5-0.5x=-4
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
5-0.5x=4
\\\\
-0.5x=4-5
\\\\
-0.5x=-1
\\\\
10(-0.5x)=10(-1)
\\\\
-5x=-10
\\\\
x=\dfrac{-10}{-5}
\\\\
x=2
\\\\\text{OR}\\\\
5-0.5x=-4
\\\\
-0.5x=-4-5
\\\\
-0.5x=-9
\\\\
10(-0.5x)=10(-9)
\\\\
-5x=-90
\\\\
x=\dfrac{-90}{-5}
\\\\
x=18
.\end{array}
Hence, $
x=\left\{ 2,18 \right\}
.$
