Question

solve $|x - 5| + 7 = 15$
a. $x = -13$ and $x = -3$
b. $x = -13$ and $x = 3$
c. $x = 13$ and $x = -3$
d. $x = 13$ and $x = -13$

Explanation:

Step1: Isolate the absolute value

Subtract 7 from both sides.
$$|x-5| = 15 - 7$$
$$|x-5| = 8$$

Step2: Split into two cases

Case 1: Inside absolute value is non-negative.
$$x-5 = 8$$
Case 2: Inside absolute value is negative.
$$x-5 = -8$$

Step3: Solve Case 1

Add 5 to both sides.
$$x = 8 + 5$$
$$x = 13$$

Step4: Solve Case 2

Add 5 to both sides.
$$x = -8 + 5$$
$$x = -3$$

Answer:

C. $x = 13$ and $x = -3$