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Beginning Algebra / Edition 7 available in Hardcover

## Overview

*For courses in beginning algebra.*

** **

**Every student can succeed.**

Elayn Martin-Gay's developmental math textbooks and video resources are motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This revision of Martin-Gay's algebra series continues her focus on students and what they need to be successful.

**Also available with MyMathLab**

MyMathLab^{®} is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

**Note:** You are purchasing a standalone product; MyMathLab does not come packaged with this content. Students, if interested in purchasing this title with MyMathLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

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## Product Details

ISBN-13: | 9780134208800 |
---|---|

Publisher: | Pearson |

Publication date: | 01/17/2016 |

Edition description: | New Edition |

Pages: | 720 |

Sales rank: | 371,439 |

Product dimensions: | 8.60(w) x 11.00(h) x 1.10(d) |

## About the Author

**Elayn Martin-Gay** has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.

Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created **Chapter Test Prep Videos** to help students during their most “teachable moment”–as they prepare for a test–along with **Instructor-to-Instructor** videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebra, and intermediate algebra.

Elayn is the author of 12 published textbooks and numerous multimedia interactive products, all specializing in developmental mathematics courses. She has also published series in Algebra 1, Algebra 2, and Geometry. She has participated as an author across a broad range of educational materials: textbooks, videos, tutorial software, and courseware. This offers an opportunity for multiple combinations for an integrated teaching and learning package, offering great consistency for the student.

## Read an Excerpt

PREFACE:

## PREFACE

### ABOUT THE BOOK

*Beginning Algebra, Third Edition* was written to provide a **solid foundation in algebra** for students who might have had no previous experience in algebra. Specific care has been taken to ensure that students have the most **up-to-date and relevant** text preparation for their next mathematics course, as well as to help students to succeed in nonmathematical courses that require a grasp of algebraic fundamentals. I have tried to achieve this by writing a user-friendly text that is keyed to objectives and contains many worked-out examples. The basic concepts of graphing are introduced early, and problem solving techniques, real-life and real-data applications, data interpretation, appropriate use of technology, mental mathematics, number sense, critical thinking, decision-making, and geometric concepts are emphasized and integrated throughout the book..

The many factors that contributed to the success of the first two editions have been retained. In preparing this edition, I considered the comments and suggestions of colleagues throughout the country, students, and many users of the prior editions. The AMATYC Crossroads in Mathematics: Standards for Introductory College Mathematics before Calculus and the MAA and NCTM standards (plus Addenda), together with advances in technology, also influenced the writing of this text.

*Beginning Algebra, Third Edition* is **part of a series of texts** that can include *Basic College Mathematics, Prealgebra, Third Edition, Intermediate Algebra, Third Edition,* or *Intermediate Algebra: A Graphing Approach, Second Edition,* and*Beginning and Intermediate Algebra, Second Edition,* a combined algebra text. Throughout the series, pedagogical features are designed to develop student proficiency in algebra and problem solving, and to prepare students for future courses.

### KEY PEDAGOGICAL FEATURES IN THE THIRD EDITION

**Readability and Connections.** I have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. When a new topic is presented, an effort has been made to **relate the new ideas to those that students may already know.** Constant reinforcement and connections within problem solving strategies, data interpretation, geometry, patterns, graphs, and situations from everyday life can help students gradually master both new and old information.

**Problem Solving Process.** This is formally introduced in Chapter 2 with a **new four-step process that is integrated throughout the text.** The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps throughout the text in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' confidence in tackling problems.

**Applications and Connections.** Every effort was made to include as many accessible, interesting, and relevant real-life applications as possible throughout the text in both worked-out examples and exercise sets. The applications **strengthen students' understanding of mathematics in the real world** and help to motivate students. They show connections to a wide range of fields including agriculture, allied health, art, astronomy, automotive ownership, aviation, biology, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, history, hobbies, labor and career issues, life science, medicine, music, nutrition, physics, political science, population, recreation, sports, technology, transportation, travel, weather, and important related mathematical areas such as geometry and statistics. (See the Index of Applications on page xxi.) Many of the applications are based on **recent and interesting real-life data.** Sources for data include newspapers, magazines, government publications, publicly held companies, special interest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included.

**Helpful Hints.** Helpful Hints, formerly Reminders, contain practical advice on applying mathematical concepts. These are found throughout the text and **strategically placed** where students are most likely to need immediate reinforcement. They are highlighted in a box for quick reference and, as appropriate, an indicator line is used to precisely identify the particular part of a problem or concept being discussed. For instance, see pages 96 and 408.

**Visual Reinforcement of Concepts.** The text contains numerous graphics, models, and illustrations to visually clarify and reinforce concepts. These include **new and updated** bar graphs, circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now **over 1,000 figures.**

**Real World Chapter Openers.** The new two-page chapter opener focuses on how math is used in a specific career, provides links to the World Wide Web, and references a "Spotlight on Decision Making" feature within the chapter for further exploration of the **career and the relevance of algebra.** For example, look at the opener for Chapter 8. The opening pages also contain a list of section titles, and an introduction to the mathematics to be studied together with mathematical connections to previous chapters in the text.

**Student Resource Icons.** At the beginning of each section, videotape, tutorial software CD Rom, Student Solutions Manual, and Study Guide icons are displayed. These icons help reinforce that these learning aids are available should students wish to use them to review concepts and skills at their own pace. These items have **direct correlation to the text** and emphasize the text's methods of solution.

**Chapter Highlights.** Found at the end of each chapter, the Chapter Highlights contain key definitions, concepts, and examples to **help students understand and retain** what they have learned.

**Chapter Project.** This feature occurs at the end of each chapter, often serving as a chapter wrap-up. For **individual or group completion,** the multi-part Chapter Project, usually hands-on or data based, allows students to problem solve, make interpretations, and to think and write about algebra.

**Functional Use of Color and New Design.** Elements of this text are highlighted with color or design to make it easier for students to read and study. Special care has been taken to use color within solutions to examples or in the art to **help clarify, distinguish, or connect concepts.** For example, look at pages 190 and 191 in Section 3.4.

### EXERCISE SETS

Each text section ends with an exercise set, usually divided into two parts. Both parts contain graded exercises. The **first part is carefully keyed** to at least one worked example in the text. Once a student has gained confidence in a skill, **the second part contains exercises not keyed to examples.** Exercises and examples marked with a *video* icon have been worked out step-by-step by the author in the videos that accompany this text.

Throughout the text exercises there is an emphasis on data and graphical interpretation via tables, charts, and graphs. The ability to interpret data and read and create a variety of types of graphs is developed gradually so students become comfortable with it. Similarly, throughout the text there is integration of geometric concepts, such as perimeter and area. Exercises and examples marked with a *geometry* icon have been identified for convenience.

Each exercise set contains one or more of the following features.

**Spotlight on Decision Making.** These unique **new, specially designed applications** help students develop their decision-making and problem solving abilities, skills useful in mathematics and in life. Appropriately placed before an exercise set begins, students have an opportunity to immediately practice and reinforce basic algebraic concepts found in the accompanying section in relevant, accessible contexts. There is an emphasis on workplace or job-related career situations (such as the decisions of a small business owner in Section 3.1, a physical therapist in Section 7.2, or a registered nurse in Section 8.5) as well as decision-making in general (such as choosing a homeowner's insurance policy in Section 2.8 or choosing a credit card in Section 5.5 or deciding when to plant flower bulbs in Section 10.6).

**Mental Mathematics.** These problems are found at the beginning of many exercise sets. They are mental warm-ups that **reinforce concepts** found in the accompanying section and increase students' confidence before they tackle an exercise set. By relying on their own mental skills, students increase not only their confidence in themselves, but also their number sense and estimation ability.

**Writing Exercises.** These exercises now found in almost every exercise set are marked with the *pencil* icon. They require students to **assimilate information** and provide a written response to explain concepts or justify their thinking. Guidelines recommended by the American Mathematical Association of Two Year Colleges (AMATYC) and other professional groups recommend incorporating writing in mathematics courses to reinforce concepts. Writing opportunities also occur within features such as Spotlight on Decision Making and Chapter Projects.

**Data and Graphical Interpretation.** Throughout the text there is an emphasis on data interpretation in exercises via tables, bar charts, line graphs, or circle graphs. The ability to interpret data and read and create a variety of graphs is **developed gradually** so students become comfortable with it. In addition, there is an appendix on mean, median, and mode together with exercises.

**Calculator Explorations and Exercises.** These optional explorations offer guided instruction, through examples and exercises, on the proper use of **scientific and graphing calculators or computer graphing utilities as tools in the mathematical problem-solving process.** Placed appropriately throughout the text, these explorations reinforce concepts or motivate discovery learning.

Additional exercises building on the skills developed in the Explorations may be found in exercise sets throughout the text, and are marked with the icon for *scientific calculator use* and with the icon for *graphing calculator use.*

**Review Exercises.** These exercises occur in each exercise set (except for those in Chapter 1). These problems are **keyed to earlier sections** and review concepts learned earlier in the text that are needed in the next section or in the next chapter. These exercises show the **links between earlier topics and later material.**

**A Look Ahead.** These exercises occur at the end of some exercise sets. This section contains examples and problems similar to those found in a subsequent algebra course. "A Look Ahead" is presented as a **natural extension of the material** and contains an example followed by advanced exercises.

In addition to the approximately 5,500 exercises within chapters, exercises may also be found in the Vocabulary Checks, Chapter Reviews, Chapter Tests, as Cumulative Reviews.

**Vocabulary Checks.** Vocabulary checks, **new to this edition,** provide an opportunity for students to become more familiar with the use of mathematical terms as they strengthen verbal skills.

**Chapter Review and Chapter Test.** The end of each chapter contains a 'review of topics introduced in the chapter. The review problems are keyed to sections. The chapter test is not keyed to sections.

**Cumulative Review.** Each chapter after the first contains a **cumulative review of all chapters beginning with the first** up through the chapter at hand. Each problem contained in the cumulative review is actually an earlier worked example in the text that is referenced in the back of the book along with the answer. Students who need to see a complete worked-out solution, with explanation, can do so by turning to the appropriate example in the text.

### KEY CONTENT FEATURES IN THE THIRD EDITION

**Overview.** This new edition retains many of the factors that have contributed to its success. Even so, **every section of the text was carefully re-examined.** Throughout the new edition you will find numerous new applications, examples, and many real-life applications and exercises. For example, look at Sections 1.9, 2.5, or 7.2. Some sections have internal re-organization to better clarify and enhance the presentation.

**Increased Integration of Geometry Concepts.** In addition to the traditional topics in beginning algebra courses, this text contains a strong emphasis on problem solving, and geometric concepts are integrated throughout. The geometry concepts presented are those most important to a students' understanding of algebra, and I have included **many applications and exercises** devoted to this topic. These are marked with the *triangle* icon. Also, geometric figures, a review of angles, lines, and special triangles, as well as a *new* review of volume and surface area are covered in the appendices. The inside front cover provides a quick reference of geometric formulas.

**Review of Real Numbers.** Chapter 1 has been streamlined and refreshed for greater efficiency and relevance. Former Sections 1.3 and 1.4 were merged to form new Section 1.4 for a smoother, more efficient flow. Chapter 1 now begins with Study Tips for Success in Mathematics (Section 1.1). **New applications** and real data enhance the chapter, especially in the reading graphs section.

**Early and Intuitive Introduction to Graphing.** As bar and line graphs are gradually introduced in Chapters 1 and 2, an emphasis is placed on the notion of paired data. This leads naturally to the concepts of ordered pair and the rectangular coordinate system introduced in Chapter 3. Chapter 3 is devoted to graphing and concepts of graphing linear equations such as slope and intercepts. **These concepts are reinforced throughout exercise sets** in subsequent chapters, helping prepare students for more work with equations in Chapter 7.

Chapter 3 has been updated, and the overall emphasis was to **better reinforce key concepts.** Reviewers have been pleased. Following user recommendations, a few of the changes are: Section 3.1 contains scattergrams of real data. Section 3.2 contains a new example and exercises on graphing and interpreting linear equations that model real data. Section 3.4 contains a new example and exercises interpreting slope as a rate of change. As usual, exercise sets progress gradually from easier to more difficult exercises.

**Increased Attention to Problem Solving.** Building on the strengths of the prior editions, a special emphasis and strong commitment is given to contemporary, accessible, and practical applications of algebra. **Real data** was drawn from a variety of sources including internet sources, magazines, newspapers, government publications, and reference books. **New Spotlight on Decision Making exercises and a new four-step problem solving process are incorporated throughout** to focus on helping to build students problem-solving skills.

**Increased Opportunities for Using Technology.** Optional explorations for a calculator or graphing calculator (or graphing utility such as Texas Instruments Interactive), are integrated appropriately **throughout the text** in Calculator Explorations features and in exercises marked with a calculator icon. The Martin-Gay companion website includes links to internet sites to allow opportunities for finding data and researching potential mathematically related careers branching from the chapter openers.

**New Examples.** Detailed step-by-step examples were added, deleted, replaced, or updated as needed. Many of these reflect real life. **Examples are used in two ways.** Often there are numbered, formal examples, and occasionally an example or application is used to introduce a topic or informally discuss the topic.

**New Exercises.** A significant amount of time was spent on the exercise sets. New exercises and examples **help address a wide range of student learning styles and abilities.** The text now includes the following types of exercises: spotlight on decision making exercises, mental math, computational exercises, real-life applications, wring exercises, multi-part exercises, review exercises, a look ahead exercises, optional calculator or graphing calculator exercises, data analysis from tables and graphs, vocabulary checks, and projects for individual or group assignment.

**Enhanced Supplements Package.** The new Third Edition is supported by a wealth of supplements designed for **added effectiveness and efficiency.** New items include the MathPro 4.0 Explorer tutorial software together with a unique video clip feature" new computerized testing system TestGen-EQ, and an expanded and improve Martin-Gay companion website. Some highlights in print materials include the addition of teaching tips in the Annotated Instructor's Edition, and an expander Instructor's Resource Manual with Tests including additional exercises and short grout activities in a ready-to-use format. Please see the list of supplements for descriptions.

*On-Line Options for Distance Learning*

For maximum convenience, Prentice Hall offers on-line interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text, *Beginning Algebra.*

**Companion Website**

Visit ...

## Table of Contents

**1. Review of Real Numbers**

1.1 Study Skill Tips for Success in Mathematics

1.2 Symbols and Sets of Numbers

1.3 Fractions and Mixed Numbers

1.4 Exponents, Order of Operations, Variable Expressions, and Equations

1.5 Adding Real Numbers

1.6 Subtracting Real Numbers

Integrated Review–Operations on Real Numbers

1.7 Multiplying and Dividing Real Numbers

1.8 Properties of Real Numbers

**2. Equations, Inequalities, and Problem Solving**

2.1 Simplifying Algebraic Expressions

2.2 The Addition Property of Equality

2.3 The Multiplication Property of Equality

2.4 Solving Linear Equations

Integrated Review–Solving Linear Equations

2.5 An Introduction to Problem Solving

2.6 Formulas and Problem Solving

2.7 Percent and Mixture Problem Solving

2.8 Further Problem Solving

2.9 Solving Linear Inequalities

**3. Graphing**

3.1 Reading Graphs and the Rectangular Coordinate System

3.2 Graphing Linear Equations

3.3 Intercepts

3.4 Slope and Rate of Change

Integrated Review–Summary on Slope and Graphing Linear Equations

3.5 Equations of Lines

3.6 Functions

**4. Solving Systems of Linear Equations and Inequalities**

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by Substitution

4.3 Solving Systems of Linear Equations by Addition

Integrated Review–Solving Systems of Equations

4.4 Systems of Linear Equations and Problem Solving

4.5 Graphing Linear Inequalities

4.6 Systems of Linear Inequalities

** **

**5. Exponents and Polynomials **

5.1 Exponents

5.2 Adding and Subtracting Polynomials

5.3 Multiplying Polynomials

5.4 Special Products

Integrated Review–Exponents and Operations on Polynomials

5.5 Negative Exponents and Scientific Notation

5.6 Dividing Polynomials

**6. Factoring Polynomials **

6.1 The Greatest Common Factor and Factoring by Grouping

6.2 Factoring Trinomials of the Form x 2 + bx + c

6.3 Factoring Trinomials of the Form ax2 + bx + c and Perfect Square Trinomials

6.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping

6.5 Factoring Binomials

Integrated Review–Choosing a Factoring Strategy

6.6 Solving Quadratic Equations by Factoring

6.7 Quadratic Equations and Problem Solving

**7. Rational Expressions **

7.1 Simplifying Rational Expressions

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with Common Denominators and Least

Common Denominator

7.4 Adding and Subtracting Rational Expressions with Unlike Denominators

7.5 Solving Equations Containing Rational Expressions

Integrated Review–Summary on Rational Expressions

7.6 Proportion and Problem Solving with Rational Equations

7.7 Variation and Problem Solving

7.8 Simplifying Complex Fractions

**8. Roots and Radicals **

8.1 Introduction to Radicals

8.2 Simplifying Radicals

8.3 Adding and Subtracting Radicals

8.4 Multiplying and Dividing Radicals

Integrated Review–Simplifying Radicals

8.5 Solving Equations Containing Radicals

8.6 Radical Equations and Problem Solving

8.7 Rational Exponents

**9. Quadratic Equations **

9.1 Solving Quadratic Equations by the Square Root Property

9.2 Solving Quadratic Equations by Completing the Square

9.3 Solving Quadratic Equations by the Quadratic Formula

Integrated Review–Summary on Solving Quadratic Equations

9.4 Complex Solutions of Quadratic Equations

9.5 Graphing Quadratic Equations

**Appendices**

A Geometry

B Additional Exercises on Proportion and Proportion Applications

C Operations on Decimals

D Mean, Median, and Mode

E Tables

Contents of Student Resources

Student Resources

Study Skills Builders

Bigger Picture–Study Guide Outline

Practice Final Exam

## Preface

## PREFACE

### ABOUT THE BOOK

*Beginning Algebra, Third Edition* was written to provide a **solid foundation in algebra** for students who might have had no previous experience in algebra. Specific care has been taken to ensure that students have the most **up-to-date and relevant** text preparation for their next mathematics course, as well as to help students to succeed in nonmathematical courses that require a grasp of algebraic fundamentals. I have tried to achieve this by writing a user-friendly text that is keyed to objectives and contains many worked-out examples. The basic concepts of graphing are introduced early, and problem solving techniques, real-life and real-data applications, data interpretation, appropriate use of technology, mental mathematics, number sense, critical thinking, decision-making, and geometric concepts are emphasized and integrated throughout the book..

The many factors that contributed to the success of the first two editions have been retained. In preparing this edition, I considered the comments and suggestions of colleagues throughout the country, students, and many users of the prior editions. The AMATYC Crossroads in Mathematics: Standards for Introductory College Mathematics before Calculus and the MAA and NCTM standards (plus Addenda), together with advances in technology, also influenced the writing of this text.

*Beginning Algebra, Third Edition* is **part of a series of texts** that can include *Basic College Mathematics, Prealgebra, Third Edition, Intermediate Algebra, Third Edition,* or *Intermediate Algebra: A Graphing Approach, Second Edition,*and*Beginning and Intermediate Algebra, Second Edition,* a combined algebra text. Throughout the series, pedagogical features are designed to develop student proficiency in algebra and problem solving, and to prepare students for future courses.

### KEY PEDAGOGICAL FEATURES IN THE THIRD EDITION

**Readability and Connections.** I have tried to make the writing style as clear as possible while still retaining the mathematical integrity of the content. When a new topic is presented, an effort has been made to **relate the new ideas to those that students may already know.** Constant reinforcement and connections within problem solving strategies, data interpretation, geometry, patterns, graphs, and situations from everyday life can help students gradually master both new and old information.

**Problem Solving Process.** This is formally introduced in Chapter 2 with a **new four-step process that is integrated throughout the text.** The four steps are Understand, Translate, Solve, and Interpret. The repeated use of these steps throughout the text in a variety of examples shows their wide applicability. Reinforcing the steps can increase students' confidence in tackling problems.

**Applications and Connections.** Every effort was made to include as many accessible, interesting, and relevant real-life applications as possible throughout the text in both worked-out examples and exercise sets. The applications **strengthen students' understanding of mathematics in the real world** and help to motivate students. They show connections to a wide range of fields including agriculture, allied health, art, astronomy, automotive ownership, aviation, biology, business, chemistry, communication, computer technology, construction, consumer affairs, demographics, earth science, education, entertainment, environmental issues, finance and economics, food service, geography, government, history, hobbies, labor and career issues, life science, medicine, music, nutrition, physics, political science, population, recreation, sports, technology, transportation, travel, weather, and important related mathematical areas such as geometry and statistics. (See the Index of Applications on page xxi.) Many of the applications are based on **recent and interesting real-life data.** Sources for data include newspapers, magazines, government publications, publicly held companies, special interest groups, research organizations, and reference books. Opportunities for obtaining your own real data are also included.

**Helpful Hints.** Helpful Hints, formerly Reminders, contain practical advice on applying mathematical concepts. These are found throughout the text and **strategically placed** where students are most likely to need immediate reinforcement. They are highlighted in a box for quick reference and, as appropriate, an indicator line is used to precisely identify the particular part of a problem or concept being discussed. For instance, see pages 96 and 408.

**Visual Reinforcement of Concepts.** The text contains numerous graphics, models, and illustrations to visually clarify and reinforce concepts. These include **new and updated** bar graphs, circle graphs in two and three dimensions, line graphs, calculator screens, application illustrations, photographs, and geometric figures. There are now **over 1,000 figures.**

**Real World Chapter Openers.** The new two-page chapter opener focuses on how math is used in a specific career, provides links to the World Wide Web, and references a "Spotlight on Decision Making" feature within the chapter for further exploration of the **career and the relevance of algebra.** For example, look at the opener for Chapter 8. The opening pages also contain a list of section titles, and an introduction to the mathematics to be studied together with mathematical connections to previous chapters in the text.

**Student Resource Icons.** At the beginning of each section, videotape, tutorial software CD Rom, Student Solutions Manual, and Study Guide icons are displayed. These icons help reinforce that these learning aids are available should students wish to use them to review concepts and skills at their own pace. These items have **direct correlation to the text** and emphasize the text's methods of solution.

**Chapter Highlights.** Found at the end of each chapter, the Chapter Highlights contain key definitions, concepts, and examples to **help students understand and retain** what they have learned.

**Chapter Project.** This feature occurs at the end of each chapter, often serving as a chapter wrap-up. For **individual or group completion,** the multi-part Chapter Project, usually hands-on or data based, allows students to problem solve, make interpretations, and to think and write about algebra.

**Functional Use of Color and New Design.** Elements of this text are highlighted with color or design to make it easier for students to read and study. Special care has been taken to use color within solutions to examples or in the art to **help clarify, distinguish, or connect concepts.** For example, look at pages 190 and 191 in Section 3.4.

### EXERCISE SETS

Each text section ends with an exercise set, usually divided into two parts. Both parts contain graded exercises. The **first part is carefully keyed** to at least one worked example in the text. Once a student has gained confidence in a skill, **the second part contains exercises not keyed to examples.** Exercises and examples marked with a *video* icon have been worked out step-by-step by the author in the videos that accompany this text.

Throughout the text exercises there is an emphasis on data and graphical interpretation via tables, charts, and graphs. The ability to interpret data and read and create a variety of types of graphs is developed gradually so students become comfortable with it. Similarly, throughout the text there is integration of geometric concepts, such as perimeter and area. Exercises and examples marked with a *geometry* icon have been identified for convenience.

Each exercise set contains one or more of the following features.

**Spotlight on Decision Making.** These unique **new, specially designed applications** help students develop their decision-making and problem solving abilities, skills useful in mathematics and in life. Appropriately placed before an exercise set begins, students have an opportunity to immediately practice and reinforce basic algebraic concepts found in the accompanying section in relevant, accessible contexts. There is an emphasis on workplace or job-related career situations (such as the decisions of a small business owner in Section 3.1, a physical therapist in Section 7.2, or a registered nurse in Section 8.5) as well as decision-making in general (such as choosing a homeowner's insurance policy in Section 2.8 or choosing a credit card in Section 5.5 or deciding when to plant flower bulbs in Section 10.6).

**Mental Mathematics.** These problems are found at the beginning of many exercise sets. They are mental warm-ups that **reinforce concepts** found in the accompanying section and increase students' confidence before they tackle an exercise set. By relying on their own mental skills, students increase not only their confidence in themselves, but also their number sense and estimation ability.

**Writing Exercises.** These exercises now found in almost every exercise set are marked with the *pencil* icon. They require students to **assimilate information** and provide a written response to explain concepts or justify their thinking. Guidelines recommended by the American Mathematical Association of Two Year Colleges (AMATYC) and other professional groups recommend incorporating writing in mathematics courses to reinforce concepts. Writing opportunities also occur within features such as Spotlight on Decision Making and Chapter Projects.

**Data and Graphical Interpretation.** Throughout the text there is an emphasis on data interpretation in exercises via tables, bar charts, line graphs, or circle graphs. The ability to interpret data and read and create a variety of graphs is **developed gradually** so students become comfortable with it. In addition, there is an appendix on mean, median, and mode together with exercises.

**Calculator Explorations and Exercises.** These optional explorations offer guided instruction, through examples and exercises, on the proper use of **scientific and graphing calculators or computer graphing utilities as tools in the mathematical problem-solving process.** Placed appropriately throughout the text, these explorations reinforce concepts or motivate discovery learning.

Additional exercises building on the skills developed in the Explorations may be found in exercise sets throughout the text, and are marked with the icon for *scientific calculator use* and with the icon for *graphing calculator use.*

**Review Exercises.** These exercises occur in each exercise set (except for those in Chapter 1). These problems are **keyed to earlier sections** and review concepts learned earlier in the text that are needed in the next section or in the next chapter. These exercises show the **links between earlier topics and later material.**

**A Look Ahead.** These exercises occur at the end of some exercise sets. This section contains examples and problems similar to those found in a subsequent algebra course. "A Look Ahead" is presented as a **natural extension of the material** and contains an example followed by advanced exercises.

In addition to the approximately 5,500 exercises within chapters, exercises may also be found in the Vocabulary Checks, Chapter Reviews, Chapter Tests, as Cumulative Reviews.

**Vocabulary Checks.** Vocabulary checks, **new to this edition,** provide an opportunity for students to become more familiar with the use of mathematical terms as they strengthen verbal skills.

**Chapter Review and Chapter Test.** The end of each chapter contains a 'review of topics introduced in the chapter. The review problems are keyed to sections. The chapter test is not keyed to sections.

**Cumulative Review.** Each chapter after the first contains a **cumulative review of all chapters beginning with the first** up through the chapter at hand. Each problem contained in the cumulative review is actually an earlier worked example in the text that is referenced in the back of the book along with the answer. Students who need to see a complete worked-out solution, with explanation, can do so by turning to the appropriate example in the text.

### KEY CONTENT FEATURES IN THE THIRD EDITION

**Overview.** This new edition retains many of the factors that have contributed to its success. Even so, **every section of the text was carefully re-examined.** Throughout the new edition you will find numerous new applications, examples, and many real-life applications and exercises. For example, look at Sections 1.9, 2.5, or 7.2. Some sections have internal re-organization to better clarify and enhance the presentation.

**Increased Integration of Geometry Concepts.** In addition to the traditional topics in beginning algebra courses, this text contains a strong emphasis on problem solving, and geometric concepts are integrated throughout. The geometry concepts presented are those most important to a students' understanding of algebra, and I have included **many applications and exercises** devoted to this topic. These are marked with the *triangle* icon. Also, geometric figures, a review of angles, lines, and special triangles, as well as a *new* review of volume and surface area are covered in the appendices. The inside front cover provides a quick reference of geometric formulas.

**Review of Real Numbers.** Chapter 1 has been streamlined and refreshed for greater efficiency and relevance. Former Sections 1.3 and 1.4 were merged to form new Section 1.4 for a smoother, more efficient flow. Chapter 1 now begins with Study Tips for Success in Mathematics (Section 1.1). **New applications** and real data enhance the chapter, especially in the reading graphs section.

**Early and Intuitive Introduction to Graphing.** As bar and line graphs are gradually introduced in Chapters 1 and 2, an emphasis is placed on the notion of paired data. This leads naturally to the concepts of ordered pair and the rectangular coordinate system introduced in Chapter 3. Chapter 3 is devoted to graphing and concepts of graphing linear equations such as slope and intercepts. **These concepts are reinforced throughout exercise sets** in subsequent chapters, helping prepare students for more work with equations in Chapter 7.

Chapter 3 has been updated, and the overall emphasis was to **better reinforce key concepts.** Reviewers have been pleased. Following user recommendations, a few of the changes are: Section 3.1 contains scattergrams of real data. Section 3.2 contains a new example and exercises on graphing and interpreting linear equations that model real data. Section 3.4 contains a new example and exercises interpreting slope as a rate of change. As usual, exercise sets progress gradually from easier to more difficult exercises.

**Increased Attention to Problem Solving.** Building on the strengths of the prior editions, a special emphasis and strong commitment is given to contemporary, accessible, and practical applications of algebra. **Real data** was drawn from a variety of sources including internet sources, magazines, newspapers, government publications, and reference books. **New Spotlight on Decision Making exercises and a new four-step problem solving process are incorporated throughout** to focus on helping to build students problem-solving skills.

**Increased Opportunities for Using Technology.** Optional explorations for a calculator or graphing calculator (or graphing utility such as Texas Instruments Interactive), are integrated appropriately **throughout the text** in Calculator Explorations features and in exercises marked with a calculator icon. The Martin-Gay companion website includes links to internet sites to allow opportunities for finding data and researching potential mathematically related careers branching from the chapter openers.

**New Examples.** Detailed step-by-step examples were added, deleted, replaced, or updated as needed. Many of these reflect real life. **Examples are used in two ways.** Often there are numbered, formal examples, and occasionally an example or application is used to introduce a topic or informally discuss the topic.

**New Exercises.** A significant amount of time was spent on the exercise sets. New exercises and examples **help address a wide range of student learning styles and abilities.** The text now includes the following types of exercises: spotlight on decision making exercises, mental math, computational exercises, real-life applications, wring exercises, multi-part exercises, review exercises, a look ahead exercises, optional calculator or graphing calculator exercises, data analysis from tables and graphs, vocabulary checks, and projects for individual or group assignment.

**Enhanced Supplements Package.** The new Third Edition is supported by a wealth of supplements designed for **added effectiveness and efficiency.** New items include the MathPro 4.0 Explorer tutorial software together with a unique video clip feature" new computerized testing system TestGen-EQ, and an expanded and improve Martin-Gay companion website. Some highlights in print materials include the addition of teaching tips in the Annotated Instructor's Edition, and an expander Instructor's Resource Manual with Tests including additional exercises and short grout activities in a ready-to-use format. Please see the list of supplements for descriptions.

*On-Line Options for Distance Learning*

For maximum convenience, Prentice Hall offers on-line interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text, *Beginning Algebra.*

**Companion Website**

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