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21 votes
21 votes
Solve: |2x − 1| < 11.

User Emiliano Sangoi
by
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1 Answer

21 votes
21 votes

STEP 1 : Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered

|2x-1| < 11

STEP 2 : Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x-1|

For the Negative case we'll use -(2x-1)

For the Positive case we'll use (2x-1)

STEP 3 : Solve the Negative Case

-(2x-1) < 11

Multiply

-2x+1 < 11

Rearrange and Add up

-2x < 10

Divide both sides by 2

-x < 5

Multiply both sides by (-1)

Remember to flip the inequality sign

x > -5

Which is the solution for the Negative Case

STEP 4 : Solve the Positive Case

(2x-1) < 11

Rearrange and Add up

2x < 12

Divide both sides by 2

x < 6

Which is the solution for the Positive Case

STEP 5 : Wrap up the solution

-5 < x < 6

Solution in Interval Notation

(-5,6) .

User Vitaliytv
by
2.3k points