# Solve for x |2x-7|-1>0 |2x-7|-1>0
Write |2x-7|-1>0 as a piecewise.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
2x-7≥0
Solve the inequality.
Add 7 to both sides of the inequality.
2x≥7
Divide each term by 2 and simplify.
Divide each term in 2x≥7 by 2.
2×2≥72
Cancel the common factor of 2.
Cancel the common factor.
2×2≥72
Divide x by 1.
x≥72
x≥72
x≥72
x≥72
In the piece where 2x-7 is non-negative, remove the absolute value.
2x-7-1>0
To find the interval for the second piece, find where the inside of the absolute value is negative.
2x-7<0
Solve the inequality.
Add 7 to both sides of the inequality.
2x<7
Divide each term by 2 and simplify.
Divide each term in 2x<7 by 2.
2×2<72
Cancel the common factor of 2.
Cancel the common factor.
2×2<72
Divide x by 1.
x<72
x<72
x<72
x<72
In the piece where 2x-7 is negative, remove the absolute value and multiply by -1.
-(2x-7)-1>0
Write as a piecewise.
{2x-7-1>0x≥72-(2x-7)-1>0x<72
Subtract 1 from -7.
{2x-8>0x≥72-(2x-7)-1>0x<72
Simplify -(2x-7)-1>0.
Simplify each term.
Apply the distributive property.
{2x-8>0x≥72-(2x)–7-1>0x<72
Multiply 2 by -1.
{2x-8>0x≥72-2x–7-1>0x<72
Multiply -1 by -7.
{2x-8>0x≥72-2x+7-1>0x<72
{2x-8>0x≥72-2x+7-1>0x<72
Subtract 1 from 7.
{2x-8>0x≥72-2x+6>0x<72
{2x-8>0x≥72-2x+6>0x<72
{2x-8>0x≥72-2x+6>0x<72
Solve 2x-8>0 when x≥72.
Solve 2x-8>0 for x.
Add 8 to both sides of the inequality.
2x>8
Divide each term by 2 and simplify.
Divide each term in 2x>8 by 2.
2×2>82
Cancel the common factor of 2.
Cancel the common factor.
2×2>82
Divide x by 1.
x>82
x>82
Divide 8 by 2.
x>4
x>4
x>4
Find the intersection of x>4 and x≥72.
x>4
x>4
Solve -2x+6>0 when x<72.
Solve -2x+6>0 for x.
Subtract 6 from both sides of the inequality.
-2x>-6
Divide each term by -2 and simplify.
Divide each term in -2x>-6 by -2. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-2x-2<-6-2
Cancel the common factor of -2.
Cancel the common factor.
-2x-2<-6-2
Divide x by 1.
x<-6-2
x<-6-2
Divide -6 by -2.
x<3
x<3
x<3
Find the intersection of x<3 and x<72.
x<3
x<3
Find the union of the solutions.
x<3 or x>4
The result can be shown in multiple forms.
Inequality Form:
x<3 or x>4
Interval Notation:
(-∞,3)∪(4,∞)
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