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# Elementary Algebra

**by**Carson, Tom; Gillespie, Ellyn

### 9780201729610

020172961X

Hardcover

1/1/2004

Addison Wesley

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## Summary

While using Elementary Algebra, Second Edition, you will find that the text focuses on building competence and confidence. The authors present the concepts, show how to do the math, and explain the reasoning behind it in a language you can understand. The text ties concepts together using the Algebra Pyramid, which will help you see the big picture of algebra. The skills Carson presents through both the Learning Strategy boxes and the Study System, introduced in the Preface and incorporated throughout the text, will not only enhance your elementary algebra experience but will also help you succeed in future college courses. Book jacket.

## Table of Contents

Preface | p. vii |

To the Student | p. xvii |

Learning Styles Inventory | p. xxiii |

Foundations of Algebra | p. 1 |

Number Sets and the Structure of Algebra | p. 2 |

Fractions | p. 11 |

Adding and Subtracting Real Numbers; Properties of Real Numbers | p. 24 |

Multiplying and Dividing Real Numbers; Properties of Real Numbers | p. 41 |

Exponents, Roots, and Order of Operations | p. 56 |

Translating Word Phrases to Expressions | p. 70 |

Evaluating and Rewriting Expressions | p. 78 |

Summary | p. 89 |

Review Exercises | p. 95 |

Practice Test | p. 99 |

Solving Linear Equations and Inequalities | p. 101 |

Equations, Formulas, and the Problem-Solving Process | p. 102 |

The Addition Principle | p. 118 |

The Multiplication Principle | p. 132 |

Applying the Principles to Formulas | p. 147 |

Translating Word Sentences to Equations | p. 153 |

Solving Linear Inequalities | p. 164 |

Summary | p. 177 |

Review Exercises | p. 182 |

Practice Test | p. 186 |

Problem Solving | p. 189 |

Ratios and Proportions | p. 190 |

Percents | p. 205 |

Problems with Two or More Unknowns | p. 221 |

Rates | p. 236 |

Investment and Mixture | p. 244 |

Summary | p. 252 |

Review Exercises | p. 257 |

Practice Test | p. 262 |

Chapters 1-3 Cumulative Review Exercises | p. 264 |

Graphing Linear Equations and Inequalities | p. 267 |

The Rectangular Coordinate System | p. 268 |

Graphing Linear Equations | p. 277 |

Graphing Using Intercepts | p. 289 |

Slope-Intercept Form | p. 299 |

Point-Slope Form | p. 313 |

Graphing Linear Inequalities | p. 327 |

Introduction to Functions and Function Notation | p. 337 |

Summary | p. 355 |

Review Exercises | p. 363 |

Practice Test | p. 370 |

Polynomials | p. 373 |

Exponents and Scientific Notation | p. 374 |

Introduction to Polynomials | p. 387 |

Adding and Subtracting Polynomials | p. 400 |

Exponent Rules and Multiplying Monomials | p. 411 |

Multiplying Polynomials; Special Products | p. 423 |

Exponent Rules and Dividing Polynomials | p. 435 |

Summary | p. 451 |

Review Exercises | p. 454 |

Practice Test | p. 458 |

Factoring | p. 459 |

Greatest Common Factor and Factoring by Grouping | p. 460 |

Factoring Trinomials of the Form x[superscript 2] + bx + c | p. 471 |

Factoring Trinomials of the Form ax[superscript 2] + bx + c, where a [not equal] 1 | p. 478 |

Factoring Special Products | p. 487 |

Strategies for Factoring | p. 496 |

Solving Quadratic Equations by Factoring | p. 502 |

Graphs of Quadratic Equations and Functions | p. 515 |

Summary | p. 525 |

Review Exercises | p. 530 |

Practice Test | p. 533 |

Chapters 1-6 Cumulative Review Exercises | p. 534 |

Rational Expressions and Equations | p. 537 |

Simplifying Rational Expressions | p. 538 |

Multiplying and Dividing Rational Expressions | p. 552 |

Adding and Subtracting Rational Expressions with the Same Denominator | p. 563 |

Adding and Subtracting Rational Expressions with Different Denominators | p. 570 |

Complex Rational Expressions | p. 582 |

Solving Equations Containing Rational Expressions | p. 591 |

Applications with Rational Expressions | p. 601 |

Summary | p. 615 |

Review Exercises | p. 622 |

Practice Test | p. 626 |

Systems of Equations | p. 629 |

Solving Systems of Linear Equations Graphically | p. 630 |

Solving Systems of Linear Equations by Substitution | p. 641 |

Solving Systems of Linear Equations by Elimination | p. 652 |

More Applications with Systems of Equations | p. 664 |

Solving Systems of Linear Inequalities | p. 678 |

Summary | p. 688 |

Review Exercises | p. 693 |

Practice Test | p. 697 |

Roots and Radicals | p. 699 |

Square Roots and Radical Expressions | p. 700 |

Multiplying and Simplifying Square Roots | p. 710 |

Dividing and Simplifying Square Roots | p. 716 |

Adding and Subtracting Square Roots | p. 727 |

Solving Radical Equations | p. 738 |

Higher Roots and Rational Exponents | p. 748 |

Summary | p. 760 |

Review Exercises | p. 764 |

Practice Test | p. 769 |

Chapters 1-9 Cumulative Review Exercises | p. 770 |

Quadratic Equations | p. 773 |

The Square Root Principle | p. 774 |

Solving Quadratic Equations by Completing the Square | p. 785 |

Solving Quadratic Equations Using the Quadratic Formula | p. 794 |

Complex Numbers | p. 806 |

Graphing Quadratic Equations | p. 815 |

Summary | p. 830 |

Review Exercises | p. 835 |

Practice Test | p. 839 |

Chapters 1-10 Cumulative Review Exercises | p. 841 |

Answers (Student edition only) | p. 1 |

Glossary | p. 1 |

Index | p. 1 |

Applications Index | p. 1 |

Photograph Credits | p. 1 |

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