Question

what are the solutions of the following equation?
$4 = 3|-2x| + 4$
choose 1 answer:
a $x = 0$ or $x = 2$
b only $x = 2$
c only $x = 0$
d there are no solutions.

Explanation:

Step1: Isolate absolute value term

Subtract 4 from both sides.
$4 - 4 = 3|-2x| + 4 - 4$
$0 = 3|-2x|$

Step2: Solve for absolute value

Divide both sides by 3.
$\frac{0}{3} = \frac{3|-2x|}{3}$
$0 = |-2x|$

Step3: Solve for x

Absolute value equals 0 only when the expression inside is 0.
$-2x = 0$
$x = \frac{0}{-2} = 0$

Answer:

C. Only $x = 0$