Answer
$x=\dfrac{-7}{2}$ or $x=\dfrac{1}{2}$
Work Step by Step
RECALL:
$|x|=a \longrightarrow x=a \text{ or } x =-a$
use the definition above to obtain
$|2x+3|=4\longrightarrow 2x+3=4 \text{ or } 2x+3=-4$
Solve each equation to obtain:
\begin{align*}
2x&=4-3 &\text{or}& &2x=-4-3\\
2x&=1 &\text{or}& & 2x=-7\\
x&=\frac{1}{2} &\text{or}& &x=-\frac{7}{2}
\end{align*}
