Question

question
solve for all values of y in simplest form.
|-7 + 4y| = 17

Explanation:

Step1: Split absolute value into two cases

For $|A|=B$, $A=B$ or $A=-B$. So:
$-7 + 4y = 17$ or $-7 + 4y = -17$

Step2: Solve first equation for y

Isolate $4y$, then solve for $y$:
$4y = 17 + 7$
$4y = 24$
$y = \frac{24}{4} = 6$

Step3: Solve second equation for y

Isolate $4y$, then solve for $y$:
$4y = -17 + 7$
$4y = -10$
$y = \frac{-10}{4} = -\frac{5}{2}$

Answer:

$y=6$ and $y=-\frac{5}{2}$