Answer
$x = -8, x = $ $\frac{2}{3}$
Work Step by Step
$\mid$$5x +1$$\mid$ $=$ $\mid$$4x - 7$$\mid$
$5x + 1 = 4x - 7$
$x = -8$
$\mid$$5x + 1$$\mid$ $=$ $\mid$$4x - 7$$\mid$
$5x + 1 = -4x +7$
$9x = 6$
$x =$ $\frac{6}{9}$
$x =$ $\frac{2}{3}$