# Algebra Examples

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

Subtract from both sides of the inequality.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

In the piece where is non-negative, remove the absolute value.

To find the interval for the second piece, find where the inside of the absolute value is negative.

Subtract from both sides of the inequality.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

In the piece where is negative, remove the absolute value and multiply by .

Write as a piecewise.

Apply the distributive property.

Multiply by .

Multiply by .