# Ch 11: High School Algebra: Working With Inequalities

### About This Chapter

## Working with Inequalities - Chapter Summary and Learning Objectives

Inequalities are simplified equations that use greater-than or less-than signs instead of a definitive equals sign and result in more than one answer. Our instructors show you the different types of inequalities and how they are graphed. Some lessons have a supplementary lesson that provides practice questions to hone your skills when working with inequalities. Additional topics covered during this chapter include how to:

- Express inequalities through compound inequalities, set notations and systems of inequalities
- Identify the differences between 1- and 2-variable inequalities
- Explain what the golden rule is for solving 1-variable absolute value inequalities
- Construct inequalities by translating number sentences
- Differentiate between OR and AND compound inequalities

Video | Objective |
---|---|

What is an Inequality? | Define what an inequality is. Explain how to graph 2-variable inequalities. |

How to Graph 1- and 2-Variable Inequalities | Explain the difference between 1- and 2-variable inequalities. Identify when to use a coordinate plane instead of a number line. |

Set Notation, Compound Inequalities and Systems of Inequalities | Demonstrate how to express inequalities through set notations, systems of inequalities and compound inequalities. |

Graphing Inequalities: Practice Problems | Get practice graphing inequalities. |

How to Solve and Graph an Absolute Value Inequality | Explain how to solve and graph 1- and 2-variable absolute value inequalities. Also explain what the golden rule is when solving 1-variable absolute value inequalities. |

Solving and Graphing Absolutely Value Inequalities: Practice Problems | Demonstrate how to solve and graph OR and AND compound inequalities as well as negative number inequalities. Define and graph a system of inequalities. |

Translating Number Sentences to Inequalities | Describe how to translate number sentences to inequalities. |

### 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 Algebra I: High School course

- High School Algebra: Solving Math Word Problems
- High School Algebra: Percent Notation
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Properties of Exponents
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Algebraic Distribution
- High School Algebra: Properties of Functions
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Quadratic Equations
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Data, Statistics, and Probability