Question

solve $|2x + 4| = 12$
a. $x = -4$ and $x = -8$
b. $x = 4$ and $x = -4$
c. $x = -4$ and $x = 8$
d. $x = 4$ and $x = -8$

Explanation:

Step1: Split absolute value equation

For $|2x+4|=12$, we get two cases:
$2x+4=12$ and $2x+4=-12$

Step2: Solve first case

Subtract 4 from both sides:
$2x=12-4=8$
Divide by 2:
$x=\frac{8}{2}=4$

Step3: Solve second case

Subtract 4 from both sides:
$2x=-12-4=-16$
Divide by 2:
$x=\frac{-16}{2}=-8$

Answer:

D. $x = 4$ and $x = -8$