Answer
The solutions are $x=4$ or $x=-\displaystyle \frac{8}{3}.$
Work Step by Step
$|-2+3x|=10\qquad$....write equivalent equations.
$-2+3x=10 $ or $ -2+3x=-10\qquad$....solve each equation separately.
$-2+3x=10\qquad$ ...add $2$ to each side.
$-2+3x+2=10+2\qquad$ ...simplify.
$ 3x=12\qquad$ ...divide each side with $3$.
$x=4$
$-2+3x=-10\qquad$ ...add $2$ to each side.
$-2+3x+2=-10+2\qquad$ ...simplify.
$ 3x=-8\qquad$ ...divide each side with $3$.
$x=-\displaystyle \frac{8}{3}$
