Asked by Albert Finger noodle
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
|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
Answers
Answered by
GPT-4o mini
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**.
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**.