Solve the following absolute value inequality.

Question

|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 this down into two separate inequalities:

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

Now solve each inequality:

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

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

Now, combining these results, we get: \[ -3 < x < 7 \]

This means the solution to the inequality \(|x - 2| < 5\) is:

\(-3 < x < 7\)

Thus, the correct response is: −3 < x < 7.