Question

solve for all values of c in simplest form. |9 + 3c| = 15

Explanation:

Step1: Split absolute value equation

For $|A|=B$, solve $A=B$ and $A=-B$:
$9 + 3c = 15$ and $9 + 3c = -15$

Step2: Solve first equation

Subtract 9 from both sides:
$3c = 15 - 9$
$3c = 6$
Divide by 3:
$c = \frac{6}{3} = 2$

Step3: Solve second equation

Subtract 9 from both sides:
$3c = -15 - 9$
$3c = -24$
Divide by 3:
$c = \frac{-24}{3} = -8$

Answer:

$c=2$ and $c=-8$