Answer
$z = -5/2$
Work Step by Step
$|X| = |Y|$ is true only if $X = Y$ OR $X = -Y$
Given
$|z + 8| = |z - 3|$
either $ z + 8= z - 3$ OR $ z + 8= -( z - 3)$
IF
$ z + 8= z - 3$
subtract $z$ from each side of the equation
$8 = -3$
Since this is false, there is no solution for $X = Y$
IF
$ z + 8= -(z - 3)$
distribute the negative on the right side
$z + 8= -z + 3$
add $z$ to each side of the equation
$2z + 8 = 3$
Subtract $8$ from each side of the equation
$2z = -5$
divide each side of the equation by $2$
$z = -5/2$
