# Solve for x |3x-1|>5 |3x-1|>5
Write |3x-1|>5 as a piecewise.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
3x-1≥0
Solve the inequality.
Add 1 to both sides of the inequality.
3x≥1
Divide each term by 3 and simplify.
Divide each term in 3x≥1 by 3.
3×3≥13
Cancel the common factor of 3.
Cancel the common factor.
3×3≥13
Divide x by 1.
x≥13
x≥13
x≥13
x≥13
In the piece where 3x-1 is non-negative, remove the absolute value.
3x-1>5
To find the interval for the second piece, find where the inside of the absolute value is negative.
3x-1<0
Solve the inequality.
Add 1 to both sides of the inequality.
3x<1
Divide each term by 3 and simplify.
Divide each term in 3x<1 by 3.
3×3<13
Cancel the common factor of 3.
Cancel the common factor.
3×3<13
Divide x by 1.
x<13
x<13
x<13
x<13
In the piece where 3x-1 is negative, remove the absolute value and multiply by -1.
-(3x-1)>5
Write as a piecewise.
{3x-1>5x≥13-(3x-1)>5x<13
Simplify -(3x-1)>5.
Apply the distributive property.
{3x-1>5x≥13-(3x)–1>5x<13
Multiply 3 by -1.
{3x-1>5x≥13-3x–1>5x<13
Multiply -1 by -1.
{3x-1>5x≥13-3x+1>5x<13
{3x-1>5x≥13-3x+1>5x<13
{3x-1>5x≥13-3x+1>5x<13
Solve 3x-1>5 when x≥13.
Solve 3x-1>5 for x.
Move all terms not containing x to the right side of the inequality.
Add 1 to both sides of the inequality.
3x>5+1
3x>6
3x>6
Divide each term by 3 and simplify.
Divide each term in 3x>6 by 3.
3×3>63
Cancel the common factor of 3.
Cancel the common factor.
3×3>63
Divide x by 1.
x>63
x>63
Divide 6 by 3.
x>2
x>2
x>2
Find the intersection of x>2 and x≥13.
x>2
x>2
Solve -3x+1>5 when x<13.
Solve -3x+1>5 for x.
Move all terms not containing x to the right side of the inequality.
Subtract 1 from both sides of the inequality.
-3x>5-1
Subtract 1 from 5.
-3x>4
-3x>4
Divide each term by -3 and simplify.
Divide each term in -3x>4 by -3. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-3x-3<4-3
Cancel the common factor of -3.
Cancel the common factor.
-3x-3<4-3
Divide x by 1.
x<4-3
x<4-3
Move the negative in front of the fraction.
x<-43
x<-43
x<-43
Find the intersection of x<-43 and x<13.
x<-43
x<-43
Find the union of the solutions.
x<-43 or x>2
The result can be shown in multiple forms.
Inequality Form:
x<-43 or x>2
Interval Notation:
(-∞,-43)∪(2,∞)
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Solve for x |3x-1|>5     