# Compound inequalities review

A compound inequality is an inequality that combines two simple inequalities. This article provides a review of how to graph and solve compound inequalities.

## What is a compound inequality?

A compound inequality is an inequality that combines two simple inequalities. Let's take a look at some examples.

### Example with "OR"

So, for example, the numbers and are both solutions of the compound inequality, but the number is not a solution.

### Example with "AND"

This compound inequality is true for values that are both greater than zero and less than four. Graphically, we represent it like this:

So, in this case, is a solution of the compound inequality, but is not because it only satisfies one of the inequalities, not both.

Note: If we wanted to, we could write this compound inequality more simply like this:

## Solving compound inequalities

### Example with "OR"

**Solve for .**

Solving the first inequality for , we get:

Solving the second inequality for , we get:

Graphically, we get:

So our compound inequality can be expressed as the simple inequality:

*Want to learn more about compound inequalities that use OR statements? Check out this video.*

### Example with "AND"

**Solve for .**

Solving the first inequality for , we get:

Solving the second inequality for , we get:

Graphically, we get:

Strangely, this means that there are no solutions to the compound inequality because there's no value of that's both greater than negative one and less than negative one.

*Want to learn more about compound inequalities that use AND statements? Check out this video.*