Answer
$x = \frac{1}{4}$ or $x=-3$
Work Step by Step
If $|u| = |v|$ , then $u = v$ or $u = -v$. Thus,
If $|5x + 2| = |4 - 3x|$, then $5x+2 = 4-3x$ or $5x+2=-(4-3x)$
Solve for $x$.
$5x+2 = 4-3x$ or $5x+2=-(4-3x)$
$5x+3x +2= 4-3x+3x$ or $5x+2-3x = -4+3x-3x$
$8x +2= 4$ or $2x+2=-4$
$8x+2-2=4-2$ or $2x+2-2=-4-2$
$8x = 2$ or $2x=-6$
$x = \frac{1}{4}$ or $x=-3$
