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# Beginning and Intermediate Algebra

**by**Martin-Gay, Elayn

4th

### 9780131444423

0131444425

Hardcover w/CD

1/1/2009

Prentice Hall

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## Summary

Elayn Martin-Gay's success as a developmental math author starts with a strong focus on mastering the basics through well-written explanations, innovative pedagogy and a meaningful, integrated program of learning resources. The revisions to this edition provide new pedagogy and resources to build reader confidence and help readers develop basic skills and understand concepts. Martin-Gay's 4-step problem solving process-Understand, Translate, Solve and Interpret-is integrated throughout. Also includes new features such as Study Skills Reminders, "Integrated Reviews", and "Concept Checks." For readers interested in learning or revisiting essential skills in beginning and intermediate algebra through the use of lively and up-to-date applications.

## Table of Contents

Preface | p. xiii |

Index of Applications | p. xxiv |

Review of Real Numbers | p. 2 |

Tips for Success in Mathematics | p. 4 |

Symbols and Sets of Numbers | p. 8 |

Fractions | p. 17 |

Introduction to Variable Expressions and Equations | p. 25 |

Adding Real Numbers | p. 34 |

Subtracting Real Numbers | p. 41 |

Multiplying and Dividing Real Numbers | p. 48 |

Properties of Real Numbers | p. 56 |

Reading Graphs | p. 61 |

Chapter 1 Project: Creating and Interpreting Graphs | p. 68 |

Chapter 1 Vocabulary Check | p. 68 |

Chapter 1 Highlights | p. 69 |

Chapter 1 Review | p. 73 |

Chapter 1 Test | p. 76 |

Equations, Inequalities, and Problem Solving | p. 78 |

Simplifying Algebraic Expressions | p. 80 |

The Addition and Multiplication Properties of Equality | p. 86 |

Solving Linear Equations | p. 96 |

An Introduction to Problem Solving | p. 104 |

Formulas and Problem Solving | p. 113 |

Percent and Problem Solving | p. 121 |

Solving Linear Inequalities | p. 130 |

Chapter 2 Project: Developing a Budget | p. 140 |

Chapter 2 Vocabulary Check | p. 141 |

Chapter 2 Highlights | p. 142 |

Chapter 2 Review | p. 146 |

Chapter 2 Test | p. 148 |

Chapter 2 Cumulative Review | p. 149 |

Graphs and Functions | p. 150 |

The Rectangular Coordinate System | p. 152 |

Graphing Equations | p. 163 |

Introduction to Functions | p. 173 |

Graphing Linear Functions | p. 188 |

The Slope of a Line | p. 195 |

Equations of Lines | p. 209 |

Graphing Linear Inequalities | p. 220 |

Chapter 3 Project: Modeling Real Data | p. 225 |

Chapter 3 Vocabulary Check | p. 226 |

Chapter 3 Highlights | p. 227 |

Chapter 3 Review | p. 232 |

Chapter 3 Test | p. 235 |

Chapter 3 Cumulative Review | p. 236 |

Solving Systems of Linear Equations | p. 238 |

Solving Systems of Linear Equations by Graphing | p. 240 |

Solving Systems of Linear Equations by Substitution | p. 247 |

Solving Systems of Linear Equations by Addition | p. 253 |

Systems of Linear Equations and Problem Solving | p. 259 |

Chapter 4 Project: Analyzing the Courses of Ships | p. 269 |

Chapter 4 Vocabulary Check | p. 270 |

Chapter 4 Highlights | p. 271 |

Chapter 4 Review | p. 274 |

Chapter 4 Test | p. 275 |

Chapter 4 Cumulative Review | p. 276 |

Exponents and Polynomials | p. 278 |

Exponents | p. 280 |

Negative Exponents and Scientific Notation | p. 290 |

Polynomial Functions and Adding and Subtracting Polynomials | p. 298 |

Multiplying Polynomials | p. 309 |

Special Products | p. 313 |

Dividing Polynomials | p. 320 |

Synthetic Division and the Remainder Theorem | p. 326 |

Chapter 5 Project: Modeling with Polynomials | p. 330 |

Chapter 5 Vocabulary Check | p. 331 |

Chapter 5 Highlights | p. 332 |

Chapter 5 Review | p. 334 |

Chapter 5 Test | p. 337 |

Chapter 5 Cumulative Review | p. 338 |

Factoring Polynomials | p. 340 |

The Greatest Common Factor and Factoring by Grouping | p. 342 |

Factoring Trinomials of the Form x[subscript 2] + bx + c | p. 348 |

Factoring Trinomials of the Form ax[subscript 2] + bx + c | p. 354 |

Factoring Binomials | p. 362 |

Choosing a Factoring Strategy | p. 368 |

Solving Quadratic Equations by Factoring | p. 373 |

Quadratic Equations and Problem Solving | p. 380 |

An Introduction to Graphing Polynomial Functions | p. 391 |

Chapter 6 Project: Choosing Among Building Options | p. 400 |

Chapter 6 Vocabulary Check | p. 400 |

Chapter 6 Highlights | p. 401 |

Chapter 6 Review | p. 405 |

Chapter 6 Test | p. 406 |

Chapter 6 Cumulative Review | p. 407 |

Rational Expressions | p. 408 |

Rational Functions and Simplifying Rational Expressions | p. 410 |

Multiplying and Dividing Rational Expressions | p. 418 |

Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator | p. 425 |

Adding and Subtracting Rational Expressions with Unlike Denominators | p. 432 |

Simplifying Complex Fractions | p. 438 |

Solving Equations Containing Rational Expressions | p. 445 |

Ratio and Proportion | p. 453 |

Rational Equations and Problem Solving | p. 459 |

Chapter 7 Project: Comparing Dosage Formulas | p. 467 |

Chapter 7 Vocabulary Check | p. 468 |

Chapter 7 Highlights | p. 469 |

Chapter 7 Review | p. 472 |

Chapter 7 Test | p. 475 |

Chapter 7 Cumulative Review | p. 476 |

Transitions to Intermediate Algebra | p. 478 |

Review Solving Equations | p. 480 |

Further Problem Solving | p. 484 |

Compound Inequalities | p. 495 |

Absolute Value Equations | p. 502 |

Absolute Value Inequalities | p. 507 |

Solving Systems of Linear Equations in Three Variables | p. 513 |

Solving Systems of Equations by Matrices | p. 521 |

Solving Systems of Equations by Determinants | p. 527 |

Chapter 8 Project: Analyzing Municipal Budgets | p. 534 |

Chapter 8 Vocabulary Check | p. 536 |

Chapter 8 Highlights | p. 536 |

Chapter 8 Review | p. 543 |

Chapter 8 Test | p. 545 |

Chapter 8 Cumulative Review | p. 546 |

Radicals, Rational Exponents, and Complex Numbers | p. 548 |

Radicals and Radical Functions | p. 550 |

Rational Exponents | p. 557 |

Simplifying Radical Expressions | p. 564 |

Adding, Subtracting, and Multiplying Radical Expressions | p. 570 |

Rationalizing Denominators and Numerators of Radical Expressions | p. 574 |

Radical Equations and Problem Solving | p. 580 |

Complex Numbers | p. 589 |

Chapter 9 Project: Calculating the Length and Period of a Pendulum | p. 596 |

Chapter 9 Vocabulary Check | p. 597 |

Chapter 9 Highlights | p. 598 |

Chapter 9 Review | p. 601 |

Chapter 9 Test | p. 603 |

Chapter 9 Cumulative Review | p. 604 |

Quadratic Equations and Functions | p. 606 |

Solving Quadratic Equations by Completing the Square | p. 608 |

Solving Quadratic Equations by the Quadratic Formula | p. 618 |

Solving Equations by Using Quadratic Methods | p. 627 |

Nonlinear Inequalities in One Variable | p. 636 |

Variation and Problem Solving | p. 643 |

Quadratic Functions and Their Graphs | p. 652 |

Further Graphing of Quadratic Functions | p. 659 |

Chapter 10 Project: Fitting a Quadratic Model to Data | p. 667 |

Chapter 10 Vocabulary Check | p. 668 |

Chapter 10 Highlights | p. 668 |

Chapter 10 Review | p. 671 |

Chapter 10 Test | p. 673 |

Chapter 10 Cumulative Review | p. 674 |

Exponential and Logarithmic Functions | p. 676 |

The Algebra of Functions; Composite Functions | p. 678 |

Inverse Functions | p. 683 |

Exponential Functions | p. 694 |

Logarithmic Functions | p. 702 |

Properties of Logarithms | p. 709 |

Common Logarithms, Natural Logarithms, and Change of Base | p. 715 |

Exponential and Logarithmic Equations and Applications | p. 721 |

Chapter 11 Project: Modeling Temperature | p. 727 |

Chapter 11 Vocabulary Check | p. 729 |

Chapter 11 Highlights | p. 729 |

Chapter 11 Review | p. 732 |

Chapter 11 Test | p. 735 |

Chapter 11 Cumulative Review | p. 736 |

Sequences, Series, and the Binomial Theorem | p. 738 |

Sequences | p. 740 |

Arithmetic and Geometric Sequences | p. 744 |

Series | p. 751 |

Partial Sums of Arithmetic and Geometric Sequences | p. 756 |

The Binomial Theorem | p. 763 |

Chapter 12 Project: Modeling College Tuition | p. 768 |

Chapter 12 Vocabulary Check | p. 769 |

Chapter 12 Highlights | p. 769 |

Chapter 12 Review | p. 771 |

Chapter 12 Test | p. 773 |

Chapter 12 Cumulative Review | p. 774 |

Conic Sections | p. 776 |

The Parabola and the Circle | p. 778 |

The Ellipse and the Hyperbola | p. 787 |

Solving Nonlinear Systems of Equations | p. 796 |

Nonlinear Inequalities and Systems of Inequalities | p. 802 |

Chapter 13 Project: Modeling Conic Sections | p. 806 |

Chapter 13 Vocabulary Check | p. 807 |

Chapter 13 Highlights | p. 808 |

Chapter 13 Review | p. 810 |

Chapter 13 Test | p. 812 |

Chapter 13 Cumulative Review | p. 813 |

Appendices | p. 815 |

Operations on Decimals | p. 815 |

Review of Angles, Lines, and Special Triangles | p. 817 |

Review of Geometric Figures | p. 825 |

Review of Volume and Surface Area | p. 829 |

Mean, Median, and Mode | p. 835 |

Introduction to Using a Graphing Utility | p. 839 |

Table of Squares and Square Roots | p. 845 |

Answers to Selected Exercises | p. 1 |

Index | p. 1 |

Photo Credits | p. 1 |

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