Answer
$y = 1$ OR $y = -1/3$
Work Step by Step
$|X| = |Y|$ is true only if $X = Y$ OR $X = -Y$
Given
$|9y + 1| = |6y + 4|$
either $9y + 1= 6y + 4$ OR $9y + 1= -(6y + 4)$
IF
$9y + 1= 6y + 4$
subtract $6y$ from each side of the equation
$3y + 1 = 4$
subtract $1$ from each side of the equation
$3y = 3$
divide each side of the equation by $3$
$y = 1$
IF
$9y + 1= -(6y + 4)$
distribute the negative on the right side
$9y + 1= -6y - 4$
add $6y$ to each side of the equation
$15y + 1 = -4$
Subtract $1$ from each side of the equation
$15y = -5$
divide each side of the equation by $15$
$y = -5/15$
$y = -1/3$
