# Ch 1: Working With Inequalities

### About This Chapter

## Working with Inequalities - Chapter Summary

The lessons in this chapter are designed to provide you with a step-by-step approach to graphing and solving mathematical inequalities. This is a progressive course of study, where each video tutorial is devoted to a specific application and builds upon the skills you learned in the previous lesson. Chapter content includes topics in:

- Graphing inequalities with one and two variables
- Set notations
- Compound and systems of inequalities
- Graphing inequalities
- Absolute value inequalities
- Writing an inequality based on a word sentence

Each of the lessons in the chapter consist of easy-to-understand graphics and visuals, along with practice problems and self-assessment quizzes that can help you see which areas you might need to review. The questions are presented in the same format as those on the GED test, so there'll be no surprises on exam day.

### GED Math Objectives

As a nationally acknowledged equivalency exam, the GED is a 4-part test that is based upon the Common Core State Standards for high school students up to and including grade 12. The mathematical reasoning portion will test your knowledge of algebraic and quantitative problem solving and will take a maximum of 90 minutes to finish. Roughly 55% of the test consists of algebra problems, with the remaining questions devoted to quantitative reasoning. The video tutorials in this chapter will cover all of the fundamental concepts and procedures found on the actual exam. Main learning objectives include:

- Define a mathematical inequality
- Work with absolute value, compound and systems of inequalities
- Translate number sentences to inequalities
- Solve and graph inequalities

The 2-part, mathematical reasoning portion of the GED determines your readiness for college or a career as well as your ability to work with numerical methods and models. The exam is taken on a computer and includes the use of an on-screen, scientific calculator during the first part of the test.

### 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. 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!

### 3. 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.

### 4. 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.

### 5. 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!

### 6. 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.

### 7. Translating Math Sentences to Inequalities

Watch this video lesson to learn how you can easily translate math sentences into inequalities. Once you know how to do this, solving word problems becomes that much easier.

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### Other Chapters

Other chapters within the Precalculus: High School course

- Absolute Value Equations
- Working with Complex Numbers
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Continuity
- Limits