# Algebra 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.
Subtract from both sides of the inequality.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
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.
Subtract from both sides of the inequality.
Divide each term in by and simplify.
Divide each term in by .
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the right side.
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 .
Apply the distributive property.
Multiply by .
Multiply by .