# 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

Step 2.1

Add to 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 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

Step 5.1

Add to 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 6

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

Step 7

Write as a piecewise.

Step 8

Step 8.1

Apply the distributive property.

Step 8.2

Multiply by .

Step 8.3

Multiply by .