# Chapter 3: Equations of Lines

**At Grade**Created by: CK-12

## Introduction

Solving equations is one of the most important mathematical skills you will learn. And in order to solve a equation, you’ll need to manipulate it to isolate its variable. That isolation may require the application of one mathematical operation or rule, two operations/rules, or more than two operations/rules.

Some day-to-day situations in which you might have to use equations are figuring out the amount a cab ride will cost you, determining the final cost of a restaurant bill with the tip included, and converting temperature from Celsius to Fahrenheit and vice versa.

In this chapter, you will learn how to apply math operations and rules to linear equations so that you can solve for a particular variable. You will also be introduced to ratio, proportion, percentage, and percent change problems.

## Chapter Outline

- 3.1. One-Step Equations and Inverse Operations
- 3.2. One-Step Equations Transformed by Multiplication-Division
- 3.3. Applications of One-Step Equations
- 3.4. Two-Step Equations and Properties of Equality
- 3.5. Multi-Step Equations with Like Terms
- 3.6. Solving Real-World Problems with Two-Step Equations
- 3.7. Multi-Step Equations
- 3.8. Solving Real-World Problems Using Multi-Step Equations
- 3.9. Equations with Variables on Both Sides
- 3.10. Ratios
- 3.11. Proportions
- 3.12. Scale and Indirect Measurement Applications
- 3.13. Conversion of Decimals, Fractions, and Percent
- 3.14. Percent Equations
- 3.15. Percent of Change

### Chapter Summary

## Summary

This chapter begins with one-step equations involving addition, subtraction, multiplication, and division. It then moves on to more sophisticated equations that require two or multiple steps to solve. Here, you’ll learn how to combine like terms. Next, it introduces equations that have variables on both sides of the equal sign. Ratios and proportions are also discussed as are problems that entail scales and indirect measurement. The chapter concludes with a thorough discussion of percentages, an introduction to the percent equation, and a collection of real-life problems that involve percent of change.