Question

Solve the following absolute value inequality.

|x−2|<5

(1 point)
Responses

−2<x<5
−2<x<5

−7<x<3
−7<x<3

−5<x<2
−5<x<2

−3<x<7

Answer 1

To solve the absolute value inequality \(|x−2|<5\), we can break it down into two separate inequalities:

1. \(x - 2 < 5\)
2. \(x - 2 > -5\)

Let's solve both inequalities:

1. For \(x - 2 < 5\):
\[
x < 5 + 2 \implies x < 7
\]

2. For \(x - 2 > -5\):
\[
x > -5 + 2 \implies x > -3
\]

Combining these results, we have:
\[
-3 < x < 7
\]

Therefore, the solution to the inequality \(|x−2|<5\) is:
\[
\boxed{-3 < x < 7}
\]

This corresponds to the response option:
−3<x<7.