Answer
$x=\left\{ -2,5 \right\}$
Work Step by Step
Since $|x|=a$ implies $x=a \text{ OR } x=-a$, then the statement $
|2x-3|=7
$ evaluates to
\begin{array}{l}
2x-3=7\\
2x=10\\
x=5
,\\\\\text{OR}\\\\
2x-3=-7\\
2x=-4\\
x=-2
.\end{array}
Hence, the solution is $
x=\left\{ -2,5 \right\}
$.