Question

solve $|x + 6| - 7 = 8$
a. $x = 9$ and $x = -9$
b. $x = 9$ and $x = -21$
c. $x = -9$ and $x = 21$
d. $x = -9$ and $x = -21$

Explanation:

Step1: Isolate the absolute value

Add 7 to both sides.
$$|x+6| - 7 + 7 = 8 + 7$$
$$|x+6| = 15$$

Step2: Split into two cases

Absolute value equals positive/negative 15.
Case 1: $x+6 = 15$
Case 2: $x+6 = -15$

Step3: Solve Case 1

Subtract 6 from both sides.
$$x = 15 - 6$$
$$x = 9$$

Step4: Solve Case 2

Subtract 6 from both sides.
$$x = -15 - 6$$
$$x = -21$$

Answer:

B. $x = 9$ and $x = -21$