Answer
The solution set is {$\frac{8}{7},4$}.
Work Step by Step
$|\frac{3x-2}{2x-3}|=2$
$\frac{3x-2}{2x-3}=2$ or $\frac{3x-2}{2x-3}=-2$
$3x-2=2(2x-3)$ or $3x-2=-2(2x-3)$
$3x-2=4x-6$ or $3x-2=-4x+6$
$3x-4x=-6+2$ or $3x+4x=6+2$
$-x=-4$ or $7x=8$
$x=4$ or $x=\frac{8}{7}$
The solution set is {$\frac{8}{7},4$}.