Question

solve: |x - 7| - 16 = -15
a. {8, 28}
b. {8, -6}
c. {-6, -8}
d. {8, 6}

Explanation:

Step1: Isolate the absolute value

Add 16 to both sides:
$$|x-7| - 16 + 16 = -15 + 16$$
$$|x-7| = 1$$

Step2: Split into two cases

Case 1: $x-7 = 1$
Case 2: $x-7 = -1$

Step3: Solve Case 1

Add 7 to both sides:
$$x = 1 + 7$$
$$x = 8$$

Step4: Solve Case 2

Add 7 to both sides:
$$x = -1 + 7$$
$$x = 6$$

Step5: Compile solution set

The solutions are $x=8$ and $x=6$, so the set is $\{8,6\}$

Answer:

D. {8, 6}