# Finite Math Examples

Step 1

Take the specified root of both sides of the inequality to eliminate the exponent on the left side.

Step 2

Step 2.1

Simplify the left side.

Step 2.1.1

Pull terms out from under the radical.

Step 2.2

Simplify the right side.

Step 2.2.1

Simplify .

Step 2.2.1.1

Rewrite as .

Step 2.2.1.2

Pull terms out from under the radical.

Step 2.2.1.3

The absolute value is the distance between a number and zero. The distance between and is .

Step 3

Step 3.1

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

Step 3.2

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

Step 3.3

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

Step 3.4

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

Step 3.5

Write as a piecewise.

Step 4

Find the intersection of and .

Step 5

Step 5.1

Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Step 5.2

Simplify the left side.

Step 5.2.1

Dividing two negative values results in a positive value.

Step 5.2.2

Divide by .

Step 5.3

Simplify the right side.

Step 5.3.1

Divide by .

Step 6

Find the union of the solutions.

or

Step 7

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

Step 8