RWM102: Equations with Variables on Both Sides | Saylor Academy

Watch these videos to see examples of how we use like terms to solve these types of equations.

Video 1: Introduction to solving an equation with variables on both sides
Video 2: Example 2: Variables on both sides
Video 3: Algebra: Linear equations 3

Source: Khan Academy, https://youtu.be/f15zA0PhSek, https://youtu.be/1c5HY3z4k8M, https://youtu.be/Zn-GbH2S0Dk
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

Last modified: Thursday, 16 January 2025, 11:29 AM

COURSE INTRODUCTION

Course Syllabus

Unit 1: Variables and Variable Expressions

1.1: Variables, Constants, and Coefficients

Identifying Variable Parts and Coefficients of Terms

1.2: Replacing Variables with Their Values

How to Write Multiplication in Algebra

Practice Evaluating Expressions in One Variable

Practice Evaluating Expressions in Two Variables

1.3: Order of Operations Review

Order of Operations

Practice Using PEMDAS

1.4: Commutative Property of Addition and Multiplication

Commutative Laws of Addition and Multiplication

1.5: Associative Property of Addition and Multiplication

Associative Laws of Addition and Multiplication

1.6: Distributive Property of Multiplication over Addition/Subtraction

Distributive Property of Multiplication over Addition

1.7: Definition and Examples of Like Terms

Like Terms

1.8: Simplifying Expressions by Combining Like Terms

Combining Like Terms

Practice Combining Like Terms with Negative Coefficients

Practice Combining Like Terms with Negative Coefficients and Distribution

Unit 2: Linear Equations

2.1: Definition of an Equation and a Solution of an Equation

Solving Linear Equations with One Variable

2.2: Addition/Subtraction Property of Equations

The Subtraction and Addition Properties of Equality

2.3: Multiplication/Division Property of Equations

The Division and Multiplication Properties of Equality

2.4: Equations of the Form x + a = b and x − a = b

Adding and Subtracting the Same Thing to Both Sides

Practice Solving One-Step Equations

2.5: Equations of the Form ax = b and x/a = b

Algebraic Equations with Multiplication and Division

Practice One-Step Equations with Multiplication and Division

2.6: Equations of the Form ax + b = c

Solving More Complicated Equations

Practice Solving Two-Step Equations

2.7: Equations of the Form ax + b = cx + d

Equations with Variables on Both Sides

Practice Solving Equations with Variables on Both Sides

2.8: Equations with Parentheses

Solving Equations with the Distributive Property

Practice Solving Multistep Equations with Distribution

2.9: Solving Literal Equation for One of the Variables

Solving Linear Equations with One Variable

Solving for One Variable

Unit 3: Word Problems

3.1: Mathematical Symbols and Expressions for Common Words and Phrases

Translating Words into Mathematical Symbols

3.2: Translating Verbal Expression into Mathematical Equations

Writing Algebraic Equations

3.3: Number Problems

Solving Algebraic Expressions and Equations Part I

3.4: Consecutive Integer Problems

Adding Consecutive and Odd Integers

Solving Algebraic Expressions and Equations Part II

3.5: General Statement Problems

Solving Linear Word Problems with Substitution

Simple Word Problems Resulting In Linear Equations

3.6: Applying the Uniform Motion Equation

Solving a Formula for a Specific Variable

3.7: Value Mixture Problems

Mixture Problems

Solving Mixture Word Problems

Practice Solving Mixture Word Problems

Solving Percent Word Problems

Practice Solving Percent Word Problems

Unit 4: Inequalities

4.1: Definition and Notation of an Inequality

Using the Language of Algebra

4.2: Graphing Inequalities on a Number Line

Plotting Inequalities on a Number Line

Introduction to Linear Inequalities

4.3: Solving One-Step Inequalities

One-Step Inequalities

One-Step Inequalities Word Problems

Practice Solving One-Step Inequalities