### 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 the Amount of Money has to be GREATER than the Total Cost of Items. In this unit, very similar to Unit 2: Equations, you will generalize the procedure for solving inequalities. You will learn that an inequality is a statement and its solution is a set of numbers that makes this statement true. You will explore which properties of inequalities are the same and which are different from the properties of equations.

**Completing this unit should take you approximately 5 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

Read the text until the section titled "The Algebra of Linear Inequalities." This part of the text is an introduction to linear equalities. As you can see from the given examples, inequalities are very similar to equations, except that they state that one expression is smaller (or greater) than another, rather than equal.

### 4.2: Graphing Inequalities on a Number Line

Read the brief encyclopedia entry and focus on the table under the title "Graphing One Variable Inequalities." In your notes, make sketches of how four different types of inequalities (in the first four rows of the table) are represented on the number line. Use these notes as a reference throughout the rest of the Unit 4.

Watch this video and take notes. In this video, Sal Khan explains the connection between algebraic inequality statement and its representation on the number line.

Complete the exercise set.

### 4.3: Solving Linear Inequalities

### 4.3.1: Solving One-Step Inequalities

Read this page and watch the videos embedded in the text. After reading the article and working through guided practice examples, complete practice problems 1-12. Once you have completed the practice problems, check your answers against the answer key.

Complete this exercise set.

### 4.3.2: Solving Multi-Step Inequalities

Complete this exercise set.

Read this page. Note that solving inequalities involves the same procedure as solving equations: simplifying both sides, bringing the variable terms to the same side, and isolating the variable. After reading the article and working through guided practice examples, complete the practice problems 1-15. Make sure to watch the embedded "Multi-Step Inequalities" video, if you need help. Once you have completed the practice problems, check your answers against the answer key.

### 4.4: Application Problems

Read the Introduction, and then scroll down to Example 3. Study the solutions for Example 3 (parts a-d), which explain how to translate the verbal statements of inequality into algebraic. Pay attention to the words such as

*at least*or*at most*, which indicate that*greater or equal*or*less or equal*notation should be used.Watch these videos and take notes. The first video is an example of a word problem that can be solved by using an inequality. The second video is an example of a real-world situation that can be described with an inequality. The third video is another, slightly more complicated example of an application of inequalities.

Complete exercises 13-16 and 24. This exercise set will allow you to assess your mastery of concepts from Unit 4. Click on the "Show Solution" link next to each problem to check your answer.