Question

Solve the following equation: 30= |- 4y + 2|

Answer 1

Suppose $-4y+2\ge0$. Then by definition of absolute value,

$|-4y+2| = -4y+2 \implies 30 = -4y+2 \implies -4y = 28 \implies \boxed{y=-7}$

On the other hand, suppose $-4y+2$. Then

$|-4y+2| = -(-4y+2) \implies 30 = 4y - 2 \implies 4y = 32 \implies \boxed{y=8}$

Recall the definition,

$|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}$