# Ch 23: AEPA Middle Grades Math: Inequalities

### About This Chapter

## AEPA Middle Grades Math: Inequalities - Chapter Summary

Review what an inequality is and how to solve and graph them as you get ready for the AEPA Middle Grades Math test. This chapter's video lessons will give you information and practice that will prepare you for exam questions on the following:

- Defining an inequality
- Graphing 1- and 2-variable inequalities
- Working with set notation, compound inequalities and systems of inequalities
- Solving and graphing absolute value inequalities
- Translating math sentences to inequalities
- Solving 1- and 2-step linear inequalities

Our expert instructors know how to help you prepare for the exam, with fun lessons on important topics. You'll get a chance to work practice problems with inequalities and can complete the lessons at your own pace.

## Objectives of the AEPA Middle Grades Math: Inequalities Chapter

Anyone who wants to teach middle grades mathematics in Arizona must have their competency assessed through the AEPA Middle Grades Math exam, which includes questions on number sense, algebra, measurement, statistics and probabilities. Questions regarding inequalities are in the Algebra and Functions section of the exam, and this section makes up 33% of the 150 total questions.

All questions are multiple choice, and ask you to solve a problem or answer a question by choosing from four possible options. The self-assessment quizzes at the end of each lesson in this chapter will give you good practice in answering these types of questions.

### 1. What is an Inequality?

An inequality is an equation that uses greater or less than symbols and is helpful in situations with multiple solutions. Explore inequalities, two-variable inequalities, and how to graph two-variable inequalities.

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

The number of variable inequalities in an equation affects how it is solved and graphed. Learn more about the properties of one-variable and two-variable inequalities and how to graph them on number lines and coordinate planes.

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

To solve problems where there are multiple points that require inequality symbols, strategies for compound equalities must be used. Learn about compound inequalities and how to represent these problems through set notation and interval notation and how to use systems of inequalities to solve these types of problems.

### 4. Graphing Inequalities: Practice Problems

Whether an inequality has one or two variables is an important distinction when graphing these types of algebraic expressions. Learn more about when to use a number line or a coordinate plane when graphing inequalities by solving some practice problems.

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

Inequalities express 'greater than' or 'less than' and are useful in situations where the maximum or minimum is known and can be solved like equations. Learn the rules for solving and graphing inequalities with one variable and two variables, including absolute values.

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

Absolute value inequalities must be split into new inequalities in order to be solved. Explore the difference between an AND and an OR compound inequality and how to solve and graph them using a system of inequalities with practice problems.

### 7. Translating Math Sentences to Inequalities

Math sentences, also called word problems, can be confusing until they are broken down into simple math problems. Learn how to translate math sentences to inequalities by defining the keywords and symbols used in inequalities and isolating the variable so the equation can be solved.

### 8. Solving One-Step Linear Inequalities

One-step linear inequalities are expressed with inequality signs (< or >) instead of equal signs (=) and can be solved in different ways. Learn how addition, subtraction, multiplication, and division are all useful tools to solve these equations.

### 9. Solving Two-Step Linear Inequalities

Two-step linear equations involve isolating the 'x' before solving the problem. Explore the steps involved to solving two step linear inequalities, and use examples to master the solving process.

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### Other Chapters

Other chapters within the AEPA Middle Grades Mathematics (NT203): Practice & Study Guide course

- AEPA Middle Grades Math: Basic Arithmetic Operations
- AEPA Middle Grades Math: Solving Word Problems
- AEPA Middle Grades Math: Properties of Numbers
- AEPA Middle Grades Math: Estimating & Rounding
- AEPA Middle Grades Math: Number Theory
- AEPA Middle Grades Math: Roots & Radical Expressions
- AEPA Middle Grades Math: Exponents & Exponential Expressions
- AEPA Middle Grades Math: Scientific Notation
- AEPA Middle Grades Math: Simplifying Expressions
- AEPA Middle Grades Math: Integers
- AEPA Middle Grades Math: Rational Numbers
- AEPA Middle Grades Math: Introduction to Fractions
- AEPA Middle Grades Math: Operations with Fractions
- AEPA Middle Grades Math: Introduction to Decimals
- AEPA Middle Grades Math: Operations with Decimals
- AEPA Middle Grades Math: Percents
- AEPA Middle Grades Math: Money & Consumer Math
- AEPA Middle Grades Math: Number Patterns & Sequences
- AEPA Middle Grades Math: Properties of Functions
- AEPA Middle Grades Math: Graphing Functions
- AEPA Middle Grades Math: Negative Numbers
- AEPA Middle Grades Math: Absolute Value
- AEPA Middle Grades Math: Factoring
- AEPA Middle Grades Math: Monomials & Polynomials
- AEPA Middle Grades Math: Writing Algebraic Expressions
- AEPA Middle Grades Math: Basic Algebraic Expressions
- AEPA Middle Grades Math: Algebraic Distribution
- AEPA Middle Grades Math: One-Step Equations
- AEPA Middle Grades Math: Two-Step Equations
- AEPA Middle Grades Math: Rational Expressions
- AEPA Middle Grades Math: The Coordinate Graph
- AEPA Middle Grades Math: Linear Equations
- AEPA Middle Grades Math: Systems of Linear Equations
- AEPA Middle Grades Math: Rates, Ratios & Proportions
- AEPA Middle Grades Math: Measurement
- AEPA Middle Grades Math: Perimeter & Area
- AEPA Middle Grades Math: Polyhedrons & Geometric Solids
- AEPA Middle Grades Math: Symmetry, Similarity & Congruence
- AEPA Middle Grades Math: Properties of Lines
- AEPA Middle Grades Math: Triangles
- AEPA Middle Grades Math: Triangle Theorems & Proofs
- AEPA Middle Grades Math: Similar Polygons
- AEPA Middle Grades Math: The Pythagorean Theorem
- AEPA Middle Grades Math: Quadrilaterals
- AEPA Middle Grades Math: Circles
- AEPA Middle Grades Math: Circular Arcs & Measurement
- AEPA Middle Grades Math: Transformations
- AEPA Middle Grades Math: Data & Graphs
- AEPA Middle Grades Math: Statistics
- AEPA Middle Grades Math: Data Collection
- AEPA Middle Grades Math: Samples & Populations
- AEPA Middle Grades Math: Probability
- AEPA Middle Grades Math: Sets
- AEPA Middle Grades Mathematics Flashcards