Answer
$\left\{-2,7\right\}$
Work Step by Step
Since $|x|=c$ (where $c$ is a positive constant) implies $x=-c$ or $x=c$, then the given equation, $
|2x-5|=9
$, implies
\begin{align*}\require{cancel}
2x-5=-9 \text{ or } 2x-5=9
.\end{align*}
Solving each equation results to
\begin{array}{l|r}
2x=-9+5 & 2x=9+5
\\
2x=-4 & 2x=14
\\\\
\dfrac{\cancel2x}{\cancel2}=-\dfrac{4}{2} & \dfrac{\cancel2x}{\cancel2}=\dfrac{14}{2}
\\\\
x=-2 & x=7
.\end{array}
Hence, the solution set of the equation, $
|2x-5|=9
$ is $
\left\{-2,7\right\}
$.
