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