Question

select the correct answer.
what is the solution to the equation |x - 4| = 17?
a. x = 21
b. x = -21 or x = 13
c. x = -13 or x = 21
d. no solutions exist.

Explanation:

Step1: Recall absolute value definition

The absolute value equation \(|a| = b\) (where \(b\geq0\)) means \(a = b\) or \(a=-b\). For \(|x - 4|=17\), we have two cases.

Step2: Solve Case 1 (\(x - 4 = 17\))

Add 4 to both sides: \(x=17 + 4=21\).

Step3: Solve Case 2 (\(x - 4=-17\))

Add 4 to both sides: \(x=-17 + 4=-13\).

Answer:

C. \(x = -13\) or \(x = 21\)