# Precalculus Examples

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.
Step 2.1
Subtract from both sides of the inequality.
Step 2.2
Divide each term in by and simplify.
Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Cancel the common factor of .
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.
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.
Step 5.1
Subtract from both sides of the inequality.
Step 5.2
Divide each term in by and simplify.
Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
Step 5.2.2.1
Cancel the common factor of .
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.
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 .
Step 8.1
Apply the distributive property.
Step 8.2
Multiply by .
Step 8.3
Multiply by .