# Chapter 3: Single Variable Equations and Inequalities

## Introduction

Here you will focus on solving equations and inequalities. You will start with basic equations that can be solved in one step and then move to more complicated equations that will require combining like terms and the distributive property. You will also learn how to solve equations with variables on both sides and multi-step equations that might have rational numbers in them. Finally, you will learn about inequalities and how solving inequalities is similar to solving equations. You will also learn how to represent your solution to an inequality graphically.

## Chapter Outline

- 3.1. Solve Equations Involving Inverse Properties of Addition and Multiplication
- 3.2. Solve Equations Involving Inverse Properties of Addition and Division
- 3.3. Solve Equations Involving Inverse Properties of Subtraction and Multiplication
- 3.4. Solve Equations Involving Inverse Properties of Subtraction and Division
- 3.5. Solve Equations Involving Combining Like Terms
- 3.6. Solve Equations with the Distributive Property
- 3.7. Solve Equations with the Distributive Property and Combining Like Terms
- 3.8. Solve Equations with a Variable on Both Sides
- 3.9. Solve Multi-Step Equations Involving Decimals
- 3.10. Solve Multi-Step Equations Involving Fractions
- 3.11. Solve Multi-Step Equations Involving Rational Numbers
- 3.12. Write and Graph Inequalities
- 3.13. Solve Inequalities Using Addition or Subtraction
- 3.14. Solve Inequalities Using Multiplication
- 3.15. Solve Inequalities Using Division
- 3.16. Solve Inequalities Involving Combining Like Terms
- 3.17. Solve Inequalities by Using the Distributive Property
- 3.18. Write and Solve Multi-Step Inequalities Given Problem Situations

### Chapter Summary

## Summary

You started by learning how to solve basic equations that required subtraction or addition and then multiplication or division to solve. These were examples of basic two-step equations. Next, you learned how to solve more complicated equations by first simplifying each side of the equation as much as possible. To simplify, you used the distributive property and combined like terms. You learned that if decimals or fractions were in the equations, you could still solve just as if these rational numbers were a whole number. Finally, you learned how to solve equations with variables on both sides by first getting all of the variables together on the same side of the equation. The big idea to remember when solving equations was: **If you perform an operation to one side of an equation, you must also perform that same operation to the other side of the equation.**

After equations you transitioned to inequalities. Inequalities are like equations except instead of an equals sign, they have an inequality symbol. While the solution to an equation is one number, the solution to an inequality is a range of numbers. Solutions to inequalities can be represented graphically on a number line. You learned that the process for solving inequalities is similar to the process for solving equations. You can perform all of the same steps except you must remember that **Whenever you divide or multiply both sides of an inequality by a negative number, you must flip your inequality symbol in order to make sure the inequality stays true.**