Answer
$x=\left\{ -\dfrac{24}{5},\dfrac{32}{5} \right\}$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $
\left|2-\dfrac{5}{2}x\right|=14
,$ is equivalent to
\begin{array}{l}\require{cancel}
2-\dfrac{5}{2}x=14 \text{ OR } 2-\dfrac{5}{2}x=-14
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2-\dfrac{5}{2}x=14
\\\\
2\left(2-\dfrac{5}{2}x\right)=(14)2
\\\\
4-5x=28
\\\\
-5x=28-4
\\\\
-5x=24
\\\\
x=\dfrac{24}{-5}
\\\\
x=-\dfrac{24}{5}
\\\\\text{ OR }\\\\
2-\dfrac{5}{2}x=-14
\\\\
2\left(2-\dfrac{5}{2}x\right)=(-14)2
\\\\
4-5x=-28
\\\\
-5x=-28-4
\\\\
-5x=-32
\\\\
x=\dfrac{-32}{-5}
\\\\
x=\dfrac{32}{5}
.\end{array}
Hence, the solutions are $
x=\left\{ -\dfrac{24}{5},\dfrac{32}{5} \right\}
.$
