Answer
$x = 9$ OR $x = -1/2$
Work Step by Step
$|X| = |Y|$ is true only if $X = Y$ OR $X = -Y$
Given
$|5x - 7| = |3x + 11|$
either $5x - 7 = 3x + 11$ OR $5x - 7 = -(3x + 11)$
IF
$5x - 7 = 3x + 11$
subtract 3x from each side of the equation
$2x - 7 = 11$
add $7$ to each side of the equation
$2x = 18$
divide each side of the equation by $2$
$x = 9$
IF
$5x - 7 = -(3x + 11)$
distribute the negative on the right side
$5x - 7 = -3x - 11$
add $3x$ to each side of the equation
$8x - 7 = -11$
add $7$ to each side of the equation
$8x = -4$
divide each side of the equation by $8$
$x = -1/2$