Answer
$\text{the interval } \left( -2,1 \right)$
Work Step by Step
Since $|x|\lt a$ implies $-a\lt x\lt a$, then the statement $
|2x+1|+4\lt7
$ evaluates to
\begin{array}{l}
|2x+1|\lt3\\
-3\lt2x+1\lt3\\
-4\lt2x\lt2\\
-2\lt x\lt1
.\end{array}
Hence, the solution set is $
\text{the interval } \left( -2,1 \right)
$.