Question

question
solve for all values of c in simplest form.
19 = |-4 + 3c|

Explanation:

Step1: Split absolute value equation

The absolute value equation $|a|=b$ (where $b>0$) splits into $a=b$ or $a=-b$. So:
$-4 + 3c = 19$ or $-4 + 3c = -19$

Step2: Solve first equation for c

Isolate $3c$, then solve for $c$:
$3c = 19 + 4$
$3c = 23$
$c = \frac{23}{3}$

Step3: Solve second equation for c

Isolate $3c$, then solve for $c$:
$3c = -19 + 4$
$3c = -15$
$c = \frac{-15}{3} = -5$

Answer:

$c = \frac{23}{3}$ or $c = -5$