About This Chapter
Equalities & Inequalities - Chapter Summary
This chapter offers an exclusive look at equalities and inequalities, and it's presented by expert instructors with a wealth of math knowledge. Review lessons to explore definitions and examples of properties of equality. Examine types of inequalities and learn how they are graphed. Also, complete practice problems that test what you've learned about inequalities. Upon completion of this chapter, you will be ready to:
- Define and describe transitive, addition, subtraction, multiplication and division properties of equality
- Describe inequalities and the symbols that represent them
- Show how to solve inequalities with decimals
- Provide the definition and describe the concept of a compound inequality
- Demonstrate how to solve and graph a system of two or more inequalities
- Exhibit an ability to translate math sentences to inequalities
- Explain the triangle inequality theorem, why it works and how it is used
Review lessons in the sequence that best suits your study needs. Access them as many times as needed until you have a good grasp of equalities and inequalities. If you need to study on the go, view the lessons from your laptop, smartphone or tablet. At any time, feel free to test your knowledge of the lessons by taking self-assessment quizzes. If you have questions about lesson topics, be sure to submit them to our experts.
1. Transitive Property of Equality: Definition & Example
After watching this video lesson, you will understand how the transitive property of equality works when you have two equations that are equal to each other. Learn the formula for this property and how you can use it to help you solve problems.
2. Addition Property of Equality: Definition & Example
After watching this video lesson, you should be able to use the addition property of equality to help you solve problems. In addition, you can learn the formula for this property.
3. Division Property of Equality: Definition & Example
In this video lesson, you will learn about the division property of equality, its formula, and how you can use it to help you solve problems where you are looking for an unknown number.
4. Multiplication Property of Equality: Definition & Example
After watching this video lesson, you will learn to use the multiplication property of equality to help you solve problems in math. You will also learn the formula for this property.
5. Subtraction Property of Equality: Definition & Example
In this video lesson, we look at the subtraction property of equality. Learn how it helps you to solve problems and how it keeps equations the same. Learn what you must do to both sides of an equation.
6. The Order of Real Numbers: Inequalities
An inequality is an operation describing how one number can be compared to another. This lesson will describe and define inequalities and the symbols used to represent them. It will also give some examples on how to work with inequalities.
7. Inequalities with Decimals
In this video lesson, we talk about solving inequalities with decimals. You will learn in what order to take your steps to solve these types of problems.
8. 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.
9. System of Inequalities: Graphing & Concept
When we need to solve a system of two or more inequalities, we graph the solution set of each one, but we put them on the same graph and see what that looks like. The overlapping shaded areas tells us where to find the solution set.
10. 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.
11. Triangle Inequality: Theorem & Proofs
In this lesson, we will use definitions and proofs to learn what the triangle inequality theorem is, why it works, and how to use it to determine if three given line segments can form a triangle.
12. 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.
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Other chapters within the NES Elementary Education Subtest 2 (103): Practice & Study Guide course
- Numeration, Number Sense, & Mathematical Operations
- Prime Numbers, Composite Numbers & Divisibility Rules
- The Least Common Multiple & Greatest Common Factor
- Place Values, Ordering Fractions & Decimals
- Rounding & Estimating Numbers
- Arithmetic & Estimation Using Decimals
- Mixed Numbers & Fractions
- Solving & Graphing Rational Numbers
- Rates, Ratios & Proportions
- Scientific Notation Math
- Strategies for Math Word Problems
- Tools for Representing Mathematical Concepts
- Calculating & Interpreting Statistical Data
- Algebraic Patterns, Equations & Functions
- Properties of Geometric Shapes
- Converting & Graphing Units of Measurement
- Area, Perimeter, Surface Area & Volume
- Life & Zoological Sciences
- Plants, Biomes & Genetics
- Taxonomy & Evolution
- Physical, Earth & Space Sciences
- Components of the Solar System & Universe
- Weather, Climate & Geologic Systems
- Scientific Method, Inquiry & Data Analysis
- Music, Drama, Theater & the Arts
- Health & Fitness in Children
- NES Elementary Education Subtest 2 Flashcards