Examples

Write the Absolute Value as Piecewise
Step 1
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Step 2
Solve the inequality.
Tap for more steps...
Step 2.1
Subtract from both sides of the inequality.
Step 2.2
Divide each term in by and simplify.
Tap for more steps...
Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
Tap for more steps...
Step 2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
Tap for more steps...
Step 2.2.3.1
Divide by .
Step 3
In the piece where is non-negative, remove the absolute value.
Step 4
To find the interval for the second piece, find where the inside of the absolute value is negative.
Step 5
Solve the inequality.
Tap for more steps...
Step 5.1
Subtract from both sides of the inequality.
Step 5.2
Divide each term in by and simplify.
Tap for more steps...
Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
Tap for more steps...
Step 5.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Divide by .
Step 5.2.3
Simplify the right side.
Tap for more steps...
Step 5.2.3.1
Divide by .
Step 6
In the piece where is negative, remove the absolute value and multiply by .
Step 7
Write as a piecewise.
Step 8
Simplify .
Tap for more steps...
Step 8.1
Apply the distributive property.
Step 8.2
Multiply by .
Step 8.3
Multiply by .
Enter YOUR Problem
Mathway requires javascript and a modern browser.