Answer
The solution set is $\{-4,3\}$.
Work Step by Step
The given equation is
$\left | 2x+1 \right |=7$
Remove absolute value bars.
$2x+1=-7$ or $ 2x+1 =7$
Substract $1$ from both sides.
$2x+1-1=-7-1$ or $ 2x+1 -1=7-1$
Simplify.
$2x=-8$ or $ 2x=6$
Divide both sides by $2$.
$\frac{2x}{2}=-\frac{8}{2}$ or $ \frac{2x}{2}=\frac{6}{2}$
Simplify.
$x=-4$ or $ x=3$.
