Answer
Choice A
Work Step by Step
Since $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c,$ then the the given inequality, $
|2x+1|\gt3
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x+1\gt3 \text{ or } 2x+1\lt-3
.\end{array}
Hence, $\text{
Choice A
.}$