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

Wanda Kane 2021-12-09 Answered
Solve the inequality. Express the answer using interval notation.
|5x-2|<6
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Expert Answer

scoollato7o
Answered 2021-12-10 Author has 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 on all parts of the inequality and then divide the whole inequality by 5 and simplify.
-6<5x-2<6
-6+2<5x-2+2<6+2
-4<5x<8
45<5x5<85
45<x<85
Hence , the solution in interval notation is (45,85).
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