# Ch 3: McDougal Littell Algebra 1 Chapter 3: Solving Linear Equations

### About This Chapter

## How It Works:

- Identify the lessons in the McDougal Littell Solving Linear Equations chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the topics on solving linear equations you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

## Students will learn how to:

- Translate one-step equations
- Collect like terms
- Solve equations that have parentheses
- Apply the distributive property
- Solve multiple-step equations
- Provide examples of ratios, rates and proportions
- Calculate with proportions and ratios
- Define percents and solve word problems that include percents
- Use the addition and multiplication principles separately and together

*McDougal Littell is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Defining, Translating, & Solving One-Step Equations

In mathematics, word problems should be translated into equations to be solved. Learn about defining, translating, and solving one-step equations and practice examples to gain more understanding, including how to identify important key words that should be used to create equations.

### 2. Solving Equations Using the Addition Principle

When solving equations using the addition principle, addition or subtraction done on one side of an equation must be done on the other side to remain the same. Learn more about this addition principle as well as three examples of it in practice.

### 3. Solving Equations Using the Multiplication Principle

When solving equations using the multiplication principle, multiplication or division must be done on both sides of the equation to stay the same. Learn more about this principle, including how to use it and some examples in multiplication and division.

### 4. Solving Equations Using Both Addition and Multiplication Principles

Solving algebraic equations often requires the use of the addition and multiplication principles. Learn about these principles and solve real-world algebraic practice problems.

### 5. Collecting Like Terms On One Side of an Equation

In algebra, like terms have the same variables, and they are raised to the same powers. Explore the definition of like terms, learn how to identify them, and review the process for collecting like terms on one side of an equation, which includes combining like terms. Work examples to gain further understanding.

### 6. Solving Equations Containing Parentheses

In solving mathematical problems, the quantities enclosed in parentheses in the equations are calculated first. Learn more about equations with parentheses, explore the property used to remove the parentheses, understand how to collect like terms, and practice solving math problems that involve parentheses.

### 7. Applying the Distributive Property to Linear Equations

In mathematics, the distributive property shows that the same answer will result whether one number is multiplied by each integer in a group of numbers or by the sum of the group of numbers. Learn about applying the distributive property to linear equations and work examples to practice the steps, including the final steps needed to solve the equations.

### 8. How to Solve Equations with Multiple Steps

Solving an algebraic equation can involve multiple steps of addition, subtraction, multiplication, and division to isolate the variable. Learn how to solve equations with multiple steps, and practice the correct order of the steps with examples.

### 9. Ratios & Rates: Definitions & Examples

In mathematics, a ratio indicates the number of times that a smaller number is contained within a larger number, while a rate expresses a ratio for two quantities measured in different units. Explore the definitions and examples of ratios and rates, learn how to compare them, and solve practice problems.

### 10. Proportion: Definition, Application & Examples

A problem with a proportion, which is a set of ratios that equal each other, can be solved with cross-multiplication. Learn about proportions, see sample problems, and learn how to calculate percent problems.

### 11. Calculations with Ratios and Proportions

Ratios allow us a way to mathematically compare two or more items, and proportions can help us find out even more information. Learn the definition of ratios and proportions, and understand how to calculate ratio and proportion problems.

### 12. Percents: Definition, Application & Examples

Percent means per hundred and is expressed with the symbol %. Explore the definition, application, and example practice problems of percents and learn how to use percents with fractions and decimals.

### 13. How to Solve Word Problems That Use Percents

To solve percent word problems, one follows four steps. Learn different ways of finding the percent, about finding the whole and the part, and percent change.

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### Other Chapters

Other chapters within the McDougal Littell Algebra 1: Online Textbook Help course

- McDougal Littell Algebra 1 Chapter 1: Expressions, Equations & Functions
- McDougal Littell Algebra 1 Chapter 2: Properties of Real Numbers
- McDougal Littell Algebra 1 Chapter 4: Graphing Linear Equations & Functions
- McDougal Littell Algebra 1 Chapter 5: Writing Linear Equations
- McDougal Littell Algebra 1 Chapter 6: Solving & Graphing Linear Inequalities
- McDougal Littell Algebra 1 Chapter 7: Systems of Linear Equations & Inequalities
- McDougal Littell Algebra 1 Chapter 8: Exponents & Exponential Functions
- McDougal Littell Algebra 1 Chapter 9: Polynomials & Factoring
- McDougal Littell Algebra 1 Chapter 10: Quadratic Equations & Functions
- McDougal Littell Algebra 1 Chapter 11: Radicals & Geometry Connections
- McDougal Littell Algebra 1 Chapter 12: Rational Equations & Functions
- McDougal Littell Algebra 1 Chapter 13: Probability & Data Analysis