Solve the inequality. Express the answer using interval notation. |3x-2|>7

angepepagiortzb

angepepagiortzb

Answered question

2021-12-04

Solve the inequality. Express the answer using interval notation.
|3x-2|>7

Answer & Explanation

Nancy Johnson

Nancy Johnson

Beginner2021-12-05Added 17 answers

Step 1
To solve the inequality |3x−2|>7, first remove the absolute value .
For the inequality of the form |x|>a ,it can be written as x>a or x<-a . Similarly inequality |3x−2|>7 can be written as 3x-2>7 or 3x-2<-7 . First solve the inequality 3x-2>7 for x by adding 2 on both sides and then finally divide both sides of inequality by 3 .
3x-2>7
3x-2+2>7+2
3x>9
3x3>93
x>3
Step 2
Now solve the inequality 3x-2<-7 for x by adding 2 on both sides and then finally divide both sides of inequality by 3 .
3x-2<-7
3x-2+2<-7+2
3x<-5
3x3<53
x<53
Hence , the solution can be written in interval notation as (,53)(3,).

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