#### Answer

$x=\left\{ -\dfrac{1}{2},\dfrac{7}{2} \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|2x-3|=4
,$ use the definition of an 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 given equation is equivalent to
\begin{array}{l}\require{cancel}
2x-3=4
\\\\\text{OR}\\\\
2x-3=-4
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x-3=4
\\\\
2x=4+3
\\\\
2x=7
\\\\
x=\dfrac{7}{2}
\\\\\text{OR}\\\\
2x-3=-4
\\\\
2x=-4+3
\\\\
2x=-1
\\\\
x=-\dfrac{1}{2}
.\end{array}
Hence, $
x=\left\{ -\dfrac{1}{2},\dfrac{7}{2} \right\}
.$