Solve the inequality. Express the answer using interval notation. |5x-2|<6

Wanda Kane

Wanda Kane

Answered question

2021-12-09

Solve the inequality. Express the answer using interval notation.
|5x-2|<6

Answer & Explanation

scoollato7o

scoollato7o

Beginner2021-12-10Added 26 answers

Step 1 
To solve |5x-2|<6 , first remove the absolute value. The inequality of the form |x|<a can also be written as -a<x<a . Similarly the inequality |5x−2|<6 can be written as -6<5x-2<6 . 
Step 2 
To solve the inequality -6<5x-2 <6, first, add 2 to every part of the inequality; next, divide it by 5 to simplify.
-6<5x-2<6 
-6+2<5x-2+2<6+2 
-4<5x<8 
45<5x5<85 
45<x<85 
Consequently, the answer in interval notation is (45,85).

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