Solve the inequality. Express the answer using interval notation.

|5x-2|<6

|5x-2|<6

Wanda Kane
2021-12-09
Answered

Solve the inequality. Express the answer using interval notation.

|5x-2|<6

|5x-2|<6

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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

$-\frac{4}{5}<\frac{5x}{5}<\frac{8}{5}$

$-\frac{4}{5}<x<\frac{8}{5}$

Hence , the solution in interval notation is$(-\frac{4}{5},\frac{8}{5})$ .

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

Hence , the solution in interval notation is

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