Solve for x |3x-4|>5

|3x-4|>5
Write |3x-4|>5 as a piecewise.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
3x-4≥0
Solve the inequality.
Add 4 to both sides of the inequality.
3x≥4
Divide each term by 3 and simplify.
Divide each term in 3x≥4 by 3.
3×3≥43
Cancel the common factor of 3.
Cancel the common factor.
3×3≥43
Divide x by 1.
x≥43
x≥43
x≥43
x≥43
In the piece where 3x-4 is non-negative, remove the absolute value.
3x-4>5
To find the interval for the second piece, find where the inside of the absolute value is negative.
3x-4<0
Solve the inequality.
Add 4 to both sides of the inequality.
3x<4
Divide each term by 3 and simplify.
Divide each term in 3x<4 by 3.
3×3<43
Cancel the common factor of 3.
Cancel the common factor.
3×3<43
Divide x by 1.
x<43
x<43
x<43
x<43
In the piece where 3x-4 is negative, remove the absolute value and multiply by -1.
-(3x-4)>5
Write as a piecewise.
{3x-4>5x≥43-(3x-4)>5x<43
Simplify -(3x-4)>5.
Apply the distributive property.
{3x-4>5x≥43-(3x)–4>5x<43
Multiply 3 by -1.
{3x-4>5x≥43-3x–4>5x<43
Multiply -1 by -4.
{3x-4>5x≥43-3x+4>5x<43
{3x-4>5x≥43-3x+4>5x<43
{3x-4>5x≥43-3x+4>5x<43
Solve 3x-4>5 when x≥43.
Solve 3x-4>5 for x.
Move all terms not containing x to the right side of the inequality.
Add 4 to both sides of the inequality.
3x>5+4
Add 5 and 4.
3x>9
3x>9
Divide each term by 3 and simplify.
Divide each term in 3x>9 by 3.
3×3>93
Cancel the common factor of 3.
Cancel the common factor.
3×3>93
Divide x by 1.
x>93
x>93
Divide 9 by 3.
x>3
x>3
x>3
Find the intersection of x>3 and x≥43.
x>3
x>3
Solve -3x+4>5 when x<43.
Solve -3x+4>5 for x.
Move all terms not containing x to the right side of the inequality.
Subtract 4 from both sides of the inequality.
-3x>5-4
Subtract 4 from 5.
-3x>1
-3x>1
Divide each term by -3 and simplify.
Divide each term in -3x>1 by -3. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
-3x-3<1-3
Cancel the common factor of -3.
Cancel the common factor.
-3x-3<1-3
Divide x by 1.
x<1-3
x<1-3
Move the negative in front of the fraction.
x<-13
x<-13
x<-13
Find the intersection of x<-13 and x<43.
x<-13
x<-13
Find the union of the solutions.
x<-13 or x>3
The result can be shown in multiple forms.
Inequality Form:
x<-13 or x>3
Interval Notation:
(-∞,-13)∪(3,∞)
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Solve for x |3x-4|>5

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