# Ch 12: Inequalities and Absolute Values

### About This Chapter

## Inequalities and Absolute Values - Chapter Summary

This chapter opens with an introduction to inequalities and their mathematical representations, such as those in algebraic, graphic, tabular and written form. You'll also learn about the domain and range of functions, or mathematical relations, including absolute values, radical, rational and polynomial, functions. At this point in the lesson, the instructor will show you how how to graph 1- and 2-variable inequalities.

In this chapter, you can also learn about absolute values, or the size of rational and irrational numbers, and find out how to evaluate and solve related expressions and problems. Additional instruction in graphing is covered, including absolute value functions, equations and inequalities. At the end of this chapter, you should be able to:

- Identify representations of mathematical functions related to inequalities and absolute values
- Discuss the limitations on the domains and ranges of mathematical functions
- Use a variety of methods to solve equations and inequalities involving functions, including algebraic methods, graphs and graphing calculators
- Model mathematical situations involving functions
- Evaluate the soundness of a solution

Our short and engaging video lessons are taught by professional instructors and are designed to expedite the learning process for complex topics. Along with the videos, you'll find transcripts with links to text lessons and additional details. When you finish the chapter, try the online self-assessment quiz to see how well you absorbed the information! If you find you need to revisit a key term or concept, you can use the video tags to review a specific part of the tutorial, without having to re-watch the entire presentation.

### 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. Finding the Domain & Range of Functions with Inequalities

In this lesson, you will learn what domain and range are and how to find them in absolute value and polynomial functions with inequalities. You will look at domain and range expressed as intervals, inequalities, and shaded graphs.

### 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. What is an Absolute Value?

When we're talking and comparing numbers, we often don't care whether its positive or negative, just how big it is. This is often called the magnitude of a number and we find it by taking the absolute value. Learn all about it here!

### 6. How to Evaluate Absolute Value Expressions

Substituting values into absolute values doesn't have to be too hard, but it can be if you're given deceiving beginning information. See if you're up to it by checking out this video!

### 7. How to Solve an Absolute Value Equation

Once you get familiar with any new operation, the next step in any algebra class is to learn how to solve equations with that operation in them. Absolute values are no different. Solve absolute value equations here!

### 8. Solving Absolute Value Practice Problems

There are many easy mistakes to make when solving absolute value equations. Learn how to avoid those mistakes here by working on examples of absolute value equations with operations on the inside and the outside of the absolute value.

### 9. Graphing Absolute Value Functions

The purpose of this lesson is to define what is meant by the absolute value of a number and then to extend this idea to define the parent function of absolute value.

### 10. How to Graph an Absolute Value and Do Transformations

Absolute value graphs normally look like the letter 'V', but transformations can change that 'V' in a number of different ways. As well as teaching you how to graph absolute values, this video will focus on a specific group of transformations called translations. Learn all about what that means here!

### 11. Graphing Absolute Value Equations: Dilations & Reflections

Although a basic absolute value graph isn't complicated, transformations can make them sufficiently confusing! In this lesson, you'll practice different transformations of absolute value graphs.

### 12. 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!

### 13. 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.

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### Other Chapters

Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course

- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Triangles
- Circles
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards