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<0`. 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}`