|2x-9|<13

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

2x-9≥0

Solve the inequality.

Add 9 to both sides of the inequality.

2x≥9

Divide each term by 2 and simplify.

Divide each term in 2x≥9 by 2.

2×2≥92

Cancel the common factor of 2.

Cancel the common factor.

2×2≥92

Divide x by 1.

x≥92

x≥92

x≥92

x≥92

In the piece where 2x-9 is non-negative, remove the absolute value.

2x-9<13

To find the interval for the second piece, find where the inside of the absolute value is negative.

2x-9<0

Solve the inequality.

Add 9 to both sides of the inequality.

2x<9

Divide each term by 2 and simplify.

Divide each term in 2x<9 by 2.

2×2<92

Cancel the common factor of 2.

Cancel the common factor.

2×2<92

Divide x by 1.

x<92

x<92

x<92

x<92

In the piece where 2x-9 is negative, remove the absolute value and multiply by -1.

-(2x-9)<13

Write as a piecewise.

{2x-9<13x≥92-(2x-9)<13x<92

Simplify -(2x-9)<13.

Apply the distributive property.

{2x-9<13x≥92-(2x)–9<13x<92

Multiply 2 by -1.

{2x-9<13x≥92-2x–9<13x<92

Multiply -1 by -9.

{2x-9<13x≥92-2x+9<13x<92

{2x-9<13x≥92-2x+9<13x<92

{2x-9<13x≥92-2x+9<13x<92

Solve 2x-9<13 for x.

Move all terms not containing x to the right side of the inequality.

Add 9 to both sides of the inequality.

2x<13+9

Add 13 and 9.

2x<22

2x<22

Divide each term by 2 and simplify.

Divide each term in 2x<22 by 2.

2×2<222

Cancel the common factor of 2.

Cancel the common factor.

2×2<222

Divide x by 1.

x<222

x<222

Divide 22 by 2.

x<11

x<11

x<11

Find the intersection of x<11 and x≥92.

92≤x<11

92≤x<11

Solve -2x+9<13 for x.

Move all terms not containing x to the right side of the inequality.

Subtract 9 from both sides of the inequality.

-2x<13-9

Subtract 9 from 13.

-2x<4

-2x<4

Divide each term by -2 and simplify.

Divide each term in -2x<4 by -2. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

-2x-2>4-2

Cancel the common factor of -2.

Cancel the common factor.

-2x-2>4-2

Divide x by 1.

x>4-2

x>4-2

Divide 4 by -2.

x>-2

x>-2

x>-2

Find the intersection of x>-2 and x<92.

-2<x<92

-2<x<92

Find the union of the solutions.

-2<x<11

The result can be shown in multiple forms.

Inequality Form:

-2<x<11

Interval Notation:

(-2,11)

<div data-graph-input="{"graphs":[{"ascii":"-2<x