# Ch 9: Solving & Graphing Linear Inequalities

### About This Chapter

## Solving & Graphing Linear Inequalities - Chapter Summary

Ensure you understand how to solve and graph linear inequalities by closely examining this chapter's bite-sized lessons. Our instructors provide the definitions and examples you need to confidently do the following in a short period of time:

- Define an inequality
- Solve linear inequality practice problems
- Graph 1- and 2-variable inequalities
- Work with set notation, compound inequalities and systems of inequalities
- Complete graphing inequality practice problems
- Solve and graph absolute value inequalities
- Define and graph the feasible region of a system of inequalities
- Solve 'and' and 'or' compound inequalities

Each lesson in this chapter is accessible in two fun formats: short videos and full transcripts. Videos are entertaining to watch and feature clickable timelines that let you skip to key topics with ease. Transcripts enable you to read the lessons as engaging texts online or print them to review at a later time. With each lesson is a multiple-choice quiz designed to test your knowledge of the concepts it covers. Get a comprehensive review of the entire chapter by taking the practice exam.

### 1. What is an Inequality?

Deciding how to spend your money can be a tricky thing. Should you save it, invest it, or enjoy it? Learn how inequalities can help you make your decision!

### 2. Solving Linear Inequalities: Practice Problems

Linear inequalities may look intimidating, but they're really not much different than linear equations. In this lesson, we'll practice solving a variety of linear inequalities.

### 3. How to Graph 1- and 2-Variable Inequalities

So an inequality is just an equation with a less than or greater than symbol. But what is the difference between 1 and 2 variable inequalities? What does have a greater than or equal to symbol change? When do you use a number line instead of a coordinate plane? Get those answers here!

### 4. Set Notation, Compound Inequalities, and Systems of Inequalities

In this lesson, we'll explore the conditions of compound inequalities and learn how to express them using set notation and interval notation. Test you knowledge afterward with a short quiz.

### 5. Graphing Inequalities: Practice Problems

If you're already pretty familiar with what inequalities are and just looking for a place to practice your skills, this is the place. This lesson covers topics like 1-variable, 2-variable, compound, and systems of inequalities.

### 6. How to Solve and Graph an Absolute Value Inequality

Taking two skills and combining them to make a more complicated problem is a classic tactic in mathematics. If you feel confident with absolute values and inequalities, see if you can tackle them with their powers combined here!

### 7. Solving and Graphing Absolute Value Inequalities: Practice Problems

Solving and graphing absolute value inequalities brings a lot of different skills together in one place. The practice problems in this video will give you a good chance to see more examples of absolute value inequalities but will also test your general algebraic knowledge.

### 8. Graphing the Feasible Region of a System of Inequalities

The feasible region of a system of inequalities is the area of the graph containing the points that satisfy all the inequalities at once. Watch this lesson to learn how to graph one.

### 9. How to Solve 'And' & 'Or' Compound Inequalities

In this lesson, we will learn the difference between a conjunction and a disjunction and how to solve and graph 'and' and 'or' inequalities on the number line.

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### Other Chapters

Other chapters within the Pennsylvania Algebra I Keystone Exam: Test Prep & Practice course

- Real Numbers & Expressions
- Understanding Exponential Expressions
- Working with Radical Expressions
- Understanding Absolute Value Expressions
- Estimation & Math Problem-Solving
- Solving Problems with Polynomials
- Solving, Writing & Graphing Linear Equations
- Solving Problems with Systems of Equations
- Understanding Function Basics
- Using Scatter Plots
- Understanding Basic Statistics
- Interpreting & Graphing Data
- Understanding the Probability of Compound Events
- Pennsylvania Algebra I Keystone Exam Flashcards