Question

solve $4|x + 6| = 16$
a. $x = -2$ and $x = -10$
b. $x = 2$ and $x = -2$
c. $x = 2$ and $x = -10$
d. $x = -2$ and $x = 10$

Explanation:

Step1: Isolate absolute value term

Divide both sides by 4:
$\frac{4|x+6|}{4} = \frac{16}{4}$
Simplify to get: $|x+6| = 4$

Step2: Set up two cases

Case 1: Inside absolute value is non-negative:
$x+6 = 4$
Case 2: Inside absolute value is negative:
$x+6 = -4$

Step3: Solve Case 1

Subtract 6 from both sides:
$x = 4 - 6$
$x = -2$

Step4: Solve Case 2

Subtract 6 from both sides:
$x = -4 - 6$
$x = -10$

Answer:

A. $x = -2$ and $x = -10$