Answer
$x=\left\{ -\dfrac{9}{2},\dfrac{11}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Given that $
f(x)=\left|\dfrac{1-2x}{5} \right|
,$ to find $x$ for which $
f(x)=2
,$ use substitution. Then use the definition of absolute value equality. Finally, use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Replacing $f(x)$ with $
2
,$ then
\begin{array}{l}\require{cancel}
f(x)=\left|\dfrac{1-2x}{5} \right|
\\\\
2=\left|\dfrac{1-2x}{5} \right|
\\\\
\left|\dfrac{1-2x}{5} \right|=2
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1-2x}{5}=2
\\\\\text{OR}\\\\
\dfrac{1-2x}{5}=-2
.\end{array}
Solving each equation above results to
\begin{array}{l}\require{cancel}
\dfrac{1-2x}{5}=2
\\\\
5\cdot\dfrac{1-2x}{5}=5\cdot2
\\\\
1-2x=10
\\\\
-2x=10-1
\\\\
-2x=9
\\\\
x=\dfrac{9}{-2}
\\\\
x=-\dfrac{9}{2}
\\\\\text{OR}\\\\
\dfrac{1-2x}{5}=-2
\\\\
5\cdot\dfrac{1-2x}{5}=5\cdot(-2)
\\\\
1-2x=-10
\\\\
-2x=-10-1
\\\\
-2x=-11
\\\\
x=\dfrac{-11}{-2}
\\\\
x=\dfrac{11}{2}
.\end{array}
Hence, $
x=\left\{ -\dfrac{9}{2},\dfrac{11}{2} \right\}
.$