# CHAPTER 7 - BASIC ALGEBRA

### OBJECTIVES

- Identify exponents and evaluate exponents using rules of exponents.
- Perform basic arithmetic operations on algebraic expressions.
- Perform basic arithmetic operations on algebraic expressions.
- Set up basic linear equations with one variable.
- Solve linear equations with one variable using various arithmetic operations.
- Create, rearrange, and use equations to solve for unknown vairables.
- Convert between exponential and logarithmic form.
- Simplify and evaluate logarithmic expressions using properties of logarithms.
- Solve exponential equations using common logarithms (log) and natural logarithms (ln).

### CHAPTER OUTLINE

7.1 Algebraic Expressions

7.3 Arithmetic Operations with Algebraic Expressions

7.5 Simple Algebraic Equations and Word Problems

7 Review Exercises

7 Self-Test Exercises

## Introduction

**Algebra** is a branch of mathematics that is used to analyze and solve practical problems by using letters and symbols, known as variables, to represent numbers. These variables, together with numbers and operations, can be combined to create algebraic expressions and equations. Algebra provides a framework from which formulas are derived to solve general problems, and helps develop logical-thinking and problem-solving skills in a systematic and analytical way. The study of algebra is required in any occupational field, including business and sciences.

In this chapter, we will learn how to evaluate and perform arithmetic with algebraic expressions, how to form and solve algebraic equations, and how to rearrange equations and formulas to isolate a particular variable.

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