### Unit 4: Inequalities

You probably use inequalities, just like equations, in everyday life without thinking about it. Every time you go to the store, you need to decide whether you have enough money to pay for the items you need to purchase. The inequality you need to solve is: your amount of money must be GREATER than the total cost of items. In this unit, we generalize the procedure we use to solve inequalities. We explore which properties of inequalities are the same and which are different from the properties of equations.

**Completing this unit should take you approximately 2 hours.**

Upon successful completion of this unit, you will be able to:

- simplify inequalities using addition and multiplication properties;
- find and graph on a number line the solution of a given linear inequality with one variable; and
- create inequalities in one variable and use them to solve problems.

### 4.1: Definition and Notation of an Inequality

Before we can begin using inequalities in equations and graphing, we need to understand the definition and language of inequalities.

Read the section on inequalities, which shows the symbols used to denote greater than and less than. You must be able to quickly recognize these two symbols. Do example 1.12 and check your answer.

### 4.2: Graphing Inequalities on a Number Line

When we think about inequalities, it can be helpful to graph them on a number line.

Watch this video.

Read these notes for more examples of how to plot inequalities.

### 4.3: Solving One-Step Inequalities

We are now ready to begin solving inequalities. In this section we will solve one-step inequalities, and in the next section we will solve more complex inequalities.

Watch this video for examples of how to work with inequalities.

Then, watch this video to see examples of how inequalities are used in real world examples.

After you watch, complete this assessment and check your answers.

### 4.4: Solving Multi-Step Inequalities

Now we are ready to solve more complex inequalities that require multiple steps.

Watch these three videos.

After you watch, complete this assessment and check your answers.