# Ch 20: ACT Math: Inequalities

### About This Chapter

## ACT Math: Inequalities - Chapter Summary

Demonstrate that you're ready for entry-level college math courses through the math section of the ACT. Working with inequalities is a crucial algebraic concept, and our engaging lessons and quizzes help you review the following aspects:

- Defining inequality
- Graphing inequalities
- Set notation
- Compound inequalities
- Systems of inequalities
- Graphing 1- and 2-variable inequalities
- Solving and graphing absolute value inequalities

Make sure that you're ready to excel in math on test day. In addition to providing information on the inequality topics listed above, this chapter also includes exercises to help you practice graphing inequalities and solving absolute value inequalities.

### ACT Math Objectives

You'll complete 60 multiple-choice questions within 60 minutes for the math section of the ACT. Most of the problems are stand-alone, but some might be in sets and refer to a common visual. Questions will address these six areas of math:

- Pre-, elementary and intermediate algebra
- Coordinate and plane geometry, in addition to trigonometry

The portion of the test that deals with algebra is 55% of the total exam. You should strive to demonstrate an understanding of the following objectives related to inequality:

- Linear equations
- Absolute value
- Solving and graphing absolute value inequalities
- Quadratic inequalities

Once you've watched our video lessons and worked your way through the self-assessment exercises and quizzes, you'll have a good idea of any areas that still need more attention.

You get four ACT scores reported for math: your total score on all 60 questions, a sub-score for pre-/elementary algebra, the sub-score for intermediate algebra/coordinate geometry and a sub-score for the combination of plane geometry and trigonometry.

### 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. 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.

### 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. 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. Compound Inequality: Definition & Concept

A compound inequality is simply the combination of two or more inequalities. In this lesson, you will learn about different ways two inequalities can be combined and how to find their solution using a number line.

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### Other Chapters

Other chapters within the ACT Prep: Practice & Study Guide course

- ACT: About the Test
- ACT English: Section Overview
- ACT English: Punctuation
- ACT English: Grammar and Usage
- ACT English: Sentence Structure
- ACT English: Parts of an Essay
- ACT English: Rhetorical Strategy
- ACT English: Organization
- ACT English: Style
- ACT Math: Overview
- ACT Math: Number & Quantity
- ACT Math: Pre-Algebra
- ACT Math: Algebraic Expressions
- ACT Math: Radicals
- ACT Math: Linear Equations
- ACT Math: Functions
- ACT Math: Types of Functions
- ACT Math: Absolute Value
- ACT Math: Matrices
- ACT Math: Probability, Combinations & Factorial
- ACT Math: Data and Statistics
- ACT Math: Exponents
- ACT Math: Polynomials and Quadratics
- ACT Math: Rational Equations and Expressions
- ACT Math: Sequences
- ACT Math: Complex Numbers
- ACT Math: Exponentials and Logarithms
- ACT Math: Coordinate Geometry
- ACT Math: Conic Sections
- ACT Math: Triangles
- ACT Math: Plane Geometry
- ACT Math: Lines and Angles
- ACT Math: Trigonometry
- ACT Science Reasoning: Overview
- ACT Science Reasoning: Fundamentals of Science
- ACT Science Reasoning: Evaluating Models
- ACT Reading: Overview
- ACT Reading: Question Types
- ACT Reading: Understanding Reading Passages
- ACT Reading: Word Meanings and Choice
- ACT Reading: Analyzing Reading Passages
- ACT Reading: Practice
- ACT Writing: Overview
- ACT Writing: Essay Skills
- ACT Writing: Planning and Writing
- ACT Writing: Advanced Writing Skills
- ACT Prep Flashcards