# Solve for x |2x-9|<13

|2x-9|<13
Write |2x-9|<13 as a piecewise.
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 when x≥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
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 when x<92.
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
Solve for x |2x-9|<13