Question

What is the solution to the inequality ∣x−5∣ < 18?

A) x < 13 or x > −7
B) x > 13 or x < −7
C) −13 < x < 23
D) x > −13 and x < 23

Answer 1

The solution to the inequality ∣x-5∣ < 18 is x > -13 and x < 23.

Step-by-step explanation:

To solve the inequality ∣x-5∣ < 18, we need to consider two cases: when x-5 is positive and when x-5 is negative.

Case 1: x-5 > 0

In this case, we have x-5 < 18, so x < 23.

Case 2: x-5 < 0

In this case, we have -(x-5) < 18, which simplifies to 5-x < 18, or x > -13.

Combining both cases, we have -13 < x < 23 as the solution to the inequality.

Therefore, the answer is D) x > -13 and x < 23.