Answer
The solution set is {$-3,-1$}.
Work Step by Step
$|\frac{2x+1}{3x+4}|=1$
$\frac{2x+1}{3x+4}=1$ or $\frac{2x+1}{3x+4}=-1$
$2x+1=1(3x+4)$ or $2x+1=-1(3x+4)$
$2x+1=3x+4$ or $2x+1=-3x-4$
$2x-3x=4-1$ or $2x+3x=-4-1$
$-x=3$ or $5x=-5$
$x=-3$ or $x=-1$
The solution set is {$-3,-1$}.