Introductory Algebra for College Students / Edition 6

by Robert F. Blitzer

Overview

The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum appeal. Blitzer’s personality shows in his writing, as he draws readers into the material through relevant and thought-provoking applications. Every Blitzer page is interesting and relevant, ensuring that students will actually use their textbook to achieve success!

Product Details

ISBN-13:	9780321758958
Publisher:	Pearson
Publication date:	01/10/2012
Edition description:	Older Edition
Pages:	768
Product dimensions:	8.70(w) x 11.00(h) x 1.30(d)

About the Author

Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob’s love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to his Developmental Algebra Series, Bob has written textbooks covering college algebra, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson Education. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

Table of Contents

1. Variables, Real Numbers, and Mathematical Models

1.1 Introduction to Algebra: Variables and Mathematical Models

1.2 Fractions in Algebra

1.3 The Real Numbers

1.4 Basic Rules of Algebra

Mid-Chapter Check Point Section 1.1–Section 1.4

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponents and Order of Operations

Chapter 1 Group Project

Chapter 1 Summary

Chapter 1 Review Exercises

Chapter 1 Test

2. Linear Equations and Inequalities in One Variable

2.1 The Addition Property of Equality

2.2 The Multiplication Property of Equality

2.3 Solving Linear Equations

2.4 Formulas and Percents

Mid-Chapter Check Point Section 2.1–Section 2.4

2.5 An Introduction to Problem Solving

2.6 Problem Solving in Geometry

2.7 Solving Linear Inequalities

Chapter 2 Group Project

Chapter 2 Summary

Chapter 2 Review Exercises

Chapter 2 Test

Cumulative Review Exercises (Chapters 1–2)

3. Linear Equations and Inequalities in Two Variables

3.1 Graphing Linear Equations in Two Variables

3.2 Graphing Linear Equations Using Intercepts

3.3 Slope

3.4 The Slope-Intercept Form of the Equation of a Line

Mid-Chapter Check Point Section 3.1–Section 3.4

3.5 The Point-Slope Form of the Equation of a Line

3.6 Linear Inequalities in Two Variables

Chapter 3 Group Project

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Test

Cumulative Review Exercises (Chapters 1–3)

4. Systems of Linear Equations and Inequalities

4.1 Solving Systems of Linear Equations by Graphing

4.2 Solving Systems of Linear Equations by the Substitution Method

4.3 Solving Systems of Linear Equations by the Addition Method

Mid-Chapter Check Point Section 4.1–Section 4.3

4.4 Problem Solving Using Systems of Equations

4.5 Systems of Linear Inequalities

Chapter 4 Group Project

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Test

Cumulative Review Exercises (Chapters 1–4)

5. Exponents and Polynomials

5.1 Adding and Subtracting Polynomials

5.2 Multiplying Polynomials

5.3 Special Products

5.4 Polynomials in Several Variables

Mid-Chapter Check Point Section 5.1–Section 5.4

5.5 Dividing Polynomials

5.6 Dividing Polynomials by Binomials

5.7 Negative Exponents and Scientific Notation

Chapter 5 Group Project

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Test

Cumulative Review Exercises (Chapters 1–5)

6. Factoring Polynomials

6.1 The Greatest Common Factor and Factoring By Grouping

6.2 Factoring Trinomials Whose Leading Coefficient Is 1

6.3 Factoring Trinomials Whose Leading Coefficient Is Not 1

Mid-Chapter Check Point Section 6.1–Section 6.3

6.4 Factoring Special Forms

6.5 A General Factoring Strategy

6.6 Solving Quadratic Equations By Factoring

Chapter 6 Group Project

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Test

Cumulative Review Exercises (Chapters 1–6)

7. Rational Expressions

7.1 Rational Expressions and Their Simplification

7.2 Multiplying and Dividing Rational Expressions

7.3 Adding and Subtracting Rational Expressions with the Same Denominator

7.4 Adding and Subtracting Rational Expressions with Different Denominators

Mid-Chapter Check Point Section 7.1–Section 7.4

7.5 Complex Rational Expressions

7.6 Solving Rational Equations

7.7 Applications Using Rational Equations and Proportions

7.8 Modeling Using Variation

Chapter 7 Group Project

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Test

Cumulative Review Exercises (Chapters 1–7)

8. Roots and Radicals

8.1 Finding Roots

8.2 Multiplying and Dividing Radicals

8.3 Operations with Radicals

Mid-Chapter Check Point Section 8.1–Section 8.3

8.4 Rationalizing the Denominator

8.5 Radical Equations

8.6 Rational Exponents

Chapter 8 Group Project

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Test

Cumulative Review Exercises (Chapters 1–8)

9. Quadratic Equations and Introduction to Functions

9.1 Solving Quadratic Equations by the Square Root Property

9.2 Solving Quadratic Equations by Completing the Square

9.3 The Quadratic Formula

Mid-Chapter Check Point Section 9.1–Section 9.3

9.4 Imaginary Numbers as Solutions of Quadratic Equations

9.5 Graphs of Quadratic Equations

9.6 Introduction to Functions

Chapter 9 Group Project

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Test

Cumulative Review Exercises (Chapters 1–9)

Appendix: Mean, Median, and Mode

Preface

Introductory Algebra for College Students, Third Edition, provides comprehensive, in-depth coverage of the topics required in a one-term course in beginning or introductory algebra. The book is written for college students who have no previous experience in algebra and for those who need a review of basic algebraic concepts. The primary goals of the Third Edition are to help students acquire a solid foundation in the basic skills of algebra and to show how algebra can model and solve authentic real-world problems.

Writing the Third Edition

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

"I cannot follow the explanations."

"The applications are not interesting."

I thought about both of these objections in writing every page of the Third Edition.

"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in the Third Edition have been extensively rewritten to make them more accessible. I have paid close attention to ensuring that the amount of detail and depth of coverage is appropriate for an introductory college algebra course. Every section has been rewritten to contain a better range of simple, intermediate, and challenging examples. Voice balloons allow for more specific annotations in examples, further clarifying procedures and concepts. A more open format gives the book a less crowded look than the Second Edition.

"The applications are not interesting." Oneof the things I enjoy most about teaching in a large urban community college is the diversity of who my students are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. Most data from the previous edition have been replaced to include data that extend as far up to the present as possible. I selected all updated real-world data to be interesting and intriguing to students. By connecting algebra to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky.

New to the Third Edition

The Third Edition is a significant revision of the Second Edition, with increased emphasis on the relevance of algebra in everyday aspects of students' lives. In addition to the book's new open look, the expanded explanations, and the updated real-world data, you will find the following new features in the Third Edition.

Readability and Level. The chapters have been extensively rewritten to make them more accessible. The Third Edition pays close attention to ensuring that the amount of detail and depth of coverage is appropriate for a liberal arts college algebra course. Every section has been rewritten to contain a better range of simple, intermediate, and challenging examples. Voice balloons allow for more specific annotations in examples, further clarifying procedures and concepts for students.

Chapter-Opening and Section-Opening Scenarios. Every chapter and every section opens with a compelling image that supports a scenario presenting a unique application of algebra in students' lives outside the classroom. Each scenario is revisited later in the chapter or section.

Check Point Examples. Each worked example is followed by a similar matched problem for the student to work while reading the material. This actively involves the student in the learning process. Answers to all Check Points are given in the answer section.

Updated Real-World Data. Real-world data is used to bring relevance to examples, discussions, and applications. Real-world data from the previous edition has been replaced to include data that extends as far up to the present as possible. Updated real-world data was selected on the basis of being interesting and intriguing to students.

Reorganized Exercise Sets. An extensive collection of exercises is included in an exercise set at the end of each section. The Third Edition organizes exercises by level within six category types: Practice Exercises, Application Exercises, Writing in Mathematics, Critical Thinking Exercises, Technology Exercises, and Review Exercises. This format makes it easy to create well-rounded homework assignments. Many new exercises have been added, with attention paid to making sure that the practice and application exercises are appropriate for the level and graded in difficulty.

Rewritten Exercise Sets. In order to update applications and take them to a new level, most application problems from the previous edition have been replaced with new exercises. At the same time, applications were carefully chosen to avoid readers becoming overwhelmed by an excessive number of options. Expanded writing exercises offer students the opportunity to write about every objective covered in each section, as well as to discuss, interpret, and give opinions about data. Each review exercises now contains the section number and example number of a similar worked-out example.

Expanded Supplements Package. The Third Edition is supported by a wealth of supplements designed for added effectiveness and efficiency. These items are described on pages xii through xiv.

Chapter Review Grids. Each chapter contains a review chart that summarizes the definitions and concepts in every section of the chapter. Examples that illustrate these key concepts are also included in the chart. Like the summary grid, review exercises are now organized by each section of the chapter.

Preserved and Expanded from the Second Edition. The features described below that helped make the Second Edition so popular continue in the Third Edition.

• Graphing. Chapter 1 contains an introduction to graphing, a topic that is integrated throughout the book. Line, bar, circle, and rectangular coordinate graphs that use real data appear in nearly every section and exercise set. Many examples and exercises use graphs to explore relationships between data and to provide ways of visualizing a problem's solution.
• Geometric Problem Solving. Chapter 3 on problem solving contains a section that teaches geometric concepts that are important to a student's understanding of algebra. There is frequent emphasis on problem solving in geometric situations, as well as on geometric models that allow students to visualize algebraic formulas.
• Thorough, Yet Optional Technology. Although the use of graphing utilities is optional, they are utilized in Using Technology boxes to enable students to visualize algebraic concepts. The use of graphing utilities is also reinforced in the technology exercises appearing in the exercise sets for those who want this option. With the book's early introduction to graphing, students can look at the calculator screens in the Using Technology boxes and gain an increased understanding of an example's solution even if they are not using a graphing utility in the course.
• Section Objectives. Learning objectives open every section. The objectives are stated in the margin at their point of use.
• Detailed Illustrative Examples. Each illustrative example is titled, making clear the purpose of the example. Examples are clearly written and provide students with detailed step-by-step solutions. No steps are omitted and each step is explained.
• Enrichment Essays. Enrichment essays provide historical, interdisciplinary, and otherwise interesting connections throughout the text.
• Study Tips. Study Tip boxes offer suggestions for problem solving, point out common student errors, and provide informal tips and suggestions. These invaluable hints appear in abundance throughout the book.
• Discovery. Discover for Yourself boxes, found throughout the text, encourage students to further explore algebraic concepts. These explorations are optional and their omission does not interfere with the continuity of the topic under consideration.
• Chapter Projects. At the end of each chapter are collaborative activities that give students the opportunity to work cooperatively as they think and talk about mathematics. Many of these exercises should result in interesting group discussions.
• End-of-Chapter Materials. The new review grids provide a focused summary and illustrative examples for each section in the chapter. A comprehensive collection of review exercises for each of the chapter's sections follows the review grid. This is followed by a chapter test. Beginning with Chapter 2, each chapter concludes with a comprehensive collection o; cumulative review exercises.

Supplements for the Instructor Printed Resources

Annotated Instructor's Edition (0-13-032841-3)

• Answers to exercises on the same text page or in Graphing Answer Section.
• Graphing Answer section contains answers to exercises requiring graphical solutions.

Instructor's Solutions Manual (0-13-034309-9)

• Step-by-step solutions for every even-numbered section exercise.
• Step-by-step solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.

Instructor's Resource Manual (0-13-034300-5)

• Notes to the Instructor
• Eight Chapter Tests per chapter (5 free response, 3 multiple choice)
• Eight Final Exams ( 4 free response, 4 multiple choice)
• Twenty additional exercises per section for added test exercises or worksheets.
• Answers to all items

Media Resources

TestGen-EQ with QuizMaster-EQ (CD ROM for IBM and Macintosh 0-13-034305-6)

• Algorithmically driven, text specific testing program.
• Networkable for administering tests and capturing grades on-line.
• Edit or add your own questions to create a nearly unlimited number of tests and worksheets.
• Use the new "Function Plotter" to create graphs.
• Tests can be easily exported to HTML so they can be posted to the Web.

Computerized Tutorial Software Course Management System

MathPro Explorer4.0

• Network version for IBM and Macintosh
• Enables instructors to create either customized or algorithmically generated practice quizzes from any section of a chapter.
• Includes an e-mail function for networked users, enabling instructors to send a message to a specific student or to an entire group.
• Network based reports and summaries for a class or student and for cumulative or selected scores are available.

MathPro 5

• Anytime. Anywhere.
• Online tutorial with enhanced class and student management features.
• Integration of TestGen-EQ allows for testing to operate within the tutorial environment.
• Course management tracking of both tutorial and testing activity.

Online Options for Distance Learning

WebCT/Blackboard/CourseCompass

• Prentice Hall offers three different on-line interactivity and delivery options for a variety of distance learning needs. Instructors may access or adopt these in conjunction with this text.

Supplements for the Student Printed Resources

Student Solutions Manual (0-13-034308-0)

• Step-by-step solutions for every odd-numbered section exercise.
• Step-by-step solutions for every (even and odd) Check Point exercise, Chapter Review exercise, Chapter Test and Cumulative Review exercise.

How to Study Mathematics

• Have your instructor contact the local Prentice Hall sales representative.

Math on the Internet: A Student's Guide

• Have your instructor contact the local Prentice Hall sales representative.

Media Resources

Computerized Tutorial Software

MathPro Explorer 4.0

• Keyed to each section of the text for text-specific tutorial exercises and instruction.
• Warm-up exercises and graded Practice Problems.
• Video clips show a problem being explained and worked out on the board.
• Algorithmically generated exercises. on-line help, glossary and summary of scores.

MathPro 5 — Anytime. Anywhere.

• Enhanced, Internet-based version of Prentice Hall's popular tutorial software.

Lecture Videos

• Keyed to each section of the text.

Digitized Lecture Videos on CD.

• Have your instructor contact the local Prentice Hall sales representative.

Prentice Hall Tutor Center

• Provides one-on-one tutorial assistance by phone, e-mail, or fax.

Companion Website

• Offers Warm-ups, Real World Activities and Chapter Quizzes.
• E-mail results to your instructor.
• Destination links provide additional opportunities to explore other related sites.

To the Student

I've written this book so that you can learn about the power of algebra and how it relates directly to your life outside the classroom. All concepts are carefully explained, important definitions and procedures are set off in boxes, and worked-out examples that present solutions in a step-by-step manner appear in every section. Each example is followed by a similar matched problem, called a Check Point, for you to try so that you can actively participate in the learning process as you read the book. (Answers to all Check Points appear in the back of the book.) Study Tips offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to applying algebra to your life to make your learning experience both interesting and relevant.

As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:

1. Attend all lectures. No book is intended to be a substitute for valuable insights and interactions that occur in the classroom. In addition to arriving for lecture on time and being prepared, you will find it useful to read the section before it is covered in lecture. This will give you a clear idea of the new material that will be discussed.

2. Read the book. Read each section with pen (or pencil) in hand. Move through the illustrative examples with great care. These worked-out examples provide a model for doing exercises in the exercise sets. As you proceed through the reading, do not give up if you do not understand every single word. Things will become clearer as you read on and see how various procedures are applied to specific worked-out examples.

3. Work problems every day and check your answers. The way to learn mathematics is by doing mathematics, which means working the Check Points and assigned exercises in the exercise sets. The more exercises you work, the better you will understand the material.

4. Prepare for chapter exams. After completing a chapter, study the summary chart, work the exercises in the Chapter Review, and work the exercises in the Chapter Test. Answers to all these exercises are given in the back of the book.

5. Use the supplements available with this book. A solutions manual containing worked-out solutions to the book's odd-numbered exercises, all review exercises, and all Check Points, a dynamic web page, and video tapes created for every section of the book are among the supplements created to help you tap into the power of mathematics. Ask your instructor or bookstore what supplements are available and where you can find them.

I wrote this book in Point Reyes National Seashore, 40 miles north of San Francisco. The park consists of 75,000 acres with miles of pristine surf-washed beaches, forested ridges, and bays flanked by white cliffs. It was my hope to convey the beauty and excitement of mathematics using nature's unspoiled beauty as a source of inspiration and creativity. Enjoy the pages that follow as you empower yourself with the algebra needed to succeed in college, your career, and in your life.

Regards,
Bob
Robert Blitzer

]]>

Editorial Reviews

This textbook introduces the basic skills of algebra and shows how algebra can model and solve real-world problems. Some of the applications are bicycle manufacturing costs, hate crime incidents, salaries, and telephone calling plans. The third edition has been rewritten to make it more accessible, and adds more supplemental resources. Annotation c. Book News, Inc., Portland, OR (booknews.com)