# Ch 17: PLACE Elementary Education: Equalities & Inequalities

### About This Chapter

## PLACE Elementary Education: Equalities and Inequalities - Chapter Summary

Review some of the math topics that you'll encounter on the PLACE Elementary Education exam though these videos that go over the properties and principles involved in mathematical equality and inequality. These lessons provide a detailed and efficient review of:

- The transitive, addition, division, multiplication, and subtraction properties of equality
- Defining inequality
- The order of real numbers
- Inequalities with decimals
- Compound and triangle inequality
- System of inequalities
- Translating math sentences to inequalities
- Graphing inequalities

The practice quizzes at the end of each lesson give you the opportunity to verify your mastery of the content before moving on to the next topic, and, if you get an answer wrong, the quiz will provide a link back to the point of the lesson dealing with the topic. If you find you're still struggling, you can ask our professional instructors questions using the help tab.

### PLACE Elementary Education: Equalities and Inequalities Chapter Objectives

The PLACE Elementary Education test measures the aptitude of potential elementary school instructors in the state of Colorado. The material in this chapter will assist you when it comes to the mathematics part of the test, which includes questions on the terminology and concepts discussed within these lessons. Use these videos on mathematical equality and inequality to give you an advantage on test day.

### 1. Transitive Property of Equality: Definition & Example

In mathematics, the transitive property of equality shows that if M is equal to N and also equal to O, then N and O must also be equal to each other. Explore the definition and examples of the transitive property of equality. Learn the formula and recognize how to use the formula and the property to solve equations.

### 2. Addition Property of Equality: Definition & Example

The addition property of equality states that when the same number is added to both sides of an equation, the equation does not change. Learn the definition of the addition property of equality in greater detail, review its formula, and apply the formula to solve example problems.

### 3. Division Property of Equality: Definition & Example

The division property of equality states that when both sides of an equation are divided by the same non-zero number, the two sides will still be equal. Learn more about the definition and formula of this property, and study some relevant examples.

### 4. Multiplication Property of Equality: Definition & Example

The multiplication property of equality states that if one side of an equation is multiplied, the other side is multiplied by the same number in order to keep the equation the same. Learn more about this formula by reviewing two examples.

### 5. Subtraction Property of Equality: Definition & Example

The subtraction property of equality states that when the same number is subtracted from both sides of an equation, the two sides will still be equal. Learn about the definition and formula of this property and explore its application through examples.

### 6. 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.

### 7. The Order of Real Numbers: Inequalities

An inequality is an operation that describes how one number can be compared to another. Explore symbols for less than and greater than, how to use inequalities, and the order of real numbers.

### 8. Inequalities with Decimals

Inequalities can include numbers with decimals and are still solvable using similar tactics as with integers. Identify the extra step in solving these equations using the provided examples of inequalities with decimals.

### 9. 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.

### 10. System of Inequalities: Graphing & Concept

The concept of a system of inequalities is solved by graphing when there are two or more inequalities. Discover how solving a system of inequalities works, and learn how to graph a single inequality, the second inequality, and the final solution.

### 11. 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.

### 12. 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.

### 13. 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.

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### Other Chapters

Other chapters within the PLACE Elementary Education: Practice & Study Guide course

- PLACE Elementary Education: Literacy Development
- PLACE Elementary Education: Reading Strategies
- PLACE Elementary Education: Communication Strategies
- PLACE Elementary Education: Conventions & Spelling
- PLACE Elementary Education: Verbs, Tenses & Agreement
- PLACE Elementary Education: Research Skills
- PLACE Elementary Education: Literary Genres & Terms
- PLACE Elementary Education: Technology Basics
- PLACE Elementary Education: Technology & Society
- PLACE Elementary Education: Scientific Investigation
- PLACE Elementary Education: Physical Science
- PLACE Elementary Education: Life Science
- PLACE Elementary Education: Earth Science
- PLACE Elementary Education: Computation
- PLACE Elementary Education: Fractions, Decimals & Percents
- PLACE Elementary Education: Patterns & Functions
- PLACE Elementary Education: Statistics & Probability
- PLACE Elementary Education: Geometry
- PLACE Elementary Education: Measurement & Calculations
- PLACE Elementary Education: Foundations of Geography
- PLACE Elementary Education: US History (1400-1877)
- PLACE Elementary Education: US History (1877-1945)
- PLACE Elementary Education: US History from 1945
- PLACE Elementary Education: Colorado History
- PLACE Elementary Education: Culture & Society
- PLACE Elementary Education: Economics
- PLACE Elementary Education: Government
- PLACE Elementary Education: Global Concerns
- PLACE Elementary Education: Social Studies Research
- PLACE Elementary Education: Principles of Music
- PLACE Elementary Education: Visual & Performing Arts
- PLACE Elementary Education: Personal Health & Safety
- PLACE Elementary Education: Public Health
- PLACE Elementary Education: Physical Fitness
- PLACE Elementary Education Flashcards