# Intermediate Algebra, 4th edition

Published by Pearson (January 1, 2017) © 2018

**Michael Sullivan**Chicago State University**Katherine R. Struve**

## eTextbook

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## MyLab

- Reach every student with personalized support
- Customize courses with ease
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For courses in Precalculus.

### Prepare. Practice. Review.

Michael Sullivan's time-tested approach focuses students on the fundamental skills they need for the course: preparing for class, practicing with homework, and reviewing the concepts. **Precalculus, 11th Edition **continues to evolve to meet the needs of today's students. The Sullivan series of texts prepares and supports students with access to help, where and when they require it. The hallmark Sullivan cycle of **continuous preparation and retention, **and the high-quality exercises that Sullivan texts are known for, give students the reinforcement they need.

**About the Book**

**Unique Sullivan examples and exercise sets distinguish the text**

**Sullivan Examples**are presented in a two-column, annotated format that explains what the authors are about to do in each step, just as a professor would. These examples read left to right, so that students understand what each step is accomplishing as they read through. (Often examples have annotations or pointers after each step, rather than before.)**Showcase Examples**take the explanations one step further with a three column format that breaks the problem solving process down for students. The left column describes a step, the middle column provides a brief annotation, as needed, to explain the step, and the right column presents the algebra. These are now covered in MyLab™ Math as well, as Guided “How To” exercises, giving students step-by-step support as they work through a problem.**The Sullivan/Struve/Mazzarella Algebra program**is designed to motivate students to “do the math”—at home or in the lab—through a full suite of resources that support a variety of learning environments.**Variety of exercise types throughout each section****Building Skills exercises**develop students’ understanding of the procedures and skills in working with the methods presented in the section.**Mixed Practice exercises**offer comprehensive skill assessment by asking students to relate multiple concepts or objectives.**Quick Check exercises**exercises follow the examples, allowing students to apply what they have just learned. These are numbered as the first problems in each section’s exercise set, making them assignable as homework, and giving an easy way refer back to the relevant examples for extra help. Quick Checks include fill-in-the-blank and True/False questions to assess students’ understanding of vocabulary and formulas. Quick Checks are numbered as part of the homework set, and are assignable in MyLab Math for instructors.

**Extra Sullivan-level Student Support**

**NEW! Quick Response (QR) codes**now appear at each section opener, at section-¿level exercises, and as part of the Chapter Tests. They link students to the videos and applets that are available for that section, giving them resources at their fingertips.**“Are You Prepared for this Section” problems**test students’ grasp of the prerequisite material for each new section.**Explaining the Concepts problems**ask students to explain concepts in their own words.**Various exercises to assist students’ understanding****Applying the Concepts exercises**ask students to apply the mathematical concepts to real-world situations.**Extending the Concepts exercises**go beyond the basics, using a variety of problems to sharpen students’ critical-thinking skills.**Synthesis Review exercises**help students grasp the “big picture” of algebra—once they have a sufficient conceptual foundation to build upon from their work in Chapters R through 4. Synthesis Review exercises ask students to perform a single operation (adding, solving, and so on) on several objects (polynomials, rational expressions, and so on). The student is then asked to discuss the similarities and differences in performing the same operation on the different objects.**Technology exercises**are included at the close of a section’s exercise set, allow for the use of graphing technology, such as graphing calculators, GeoGebra, or Demos to solve problems. These exercises are

**About the Book**

**Extra Sullivan-level Student Support**

**Quick Response (QR) codes**now appear at each section opener, at section-¿level exercises, and as part of the Chapter Tests. They link students to the videos and applets that are available for that section, giving them resources at their fingertips.

**Also available with MyLab Math.**

MyLab™ Math 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.

**Video Program**gives students just-in-time help at home, in the lab, or to go through a wealth of video resources in the MyLab Math course. Video resources include:**Author-in-Action videos**feature author Mike Sullivan delivering in-class lectures and interacting with a live student audience. Students have access to a master teacher regardless of where and when they are studying.**Example-level solution clips****Chapter Test Prep videos**help students during their most teachable moment–when they are preparing for a test with step-by-step solutions for the exercises found in each Chapter Test.**How To exercises**ask students to test their knowledge and are truly assignable in MyLab Math. These Guided Exercises walk students through each step of the problem-solving process, giving them a guided, step-by-step learning experience. These exercises were written and developed by Jessica Bernards and Wendy Fresh who are contributors to the author team. Students are required to respond to questions as the steps to solving problems are developed. This is similar to the Help Me Solve This feature in MyLab Math. They keep students engaged while developing their conceptual understanding.**GeoGebra applets**have been developed by Jessica Bernards and Wendy Fresh along with discovery activities to allow students to develop understanding of mathematical concepts through experiential learning. These enable students to explore and manipulate math in a visual and tangible way. The Geogebra applets may be found in MyLab Math or directly at www.pearsonhighered.com/SullivanApplets.

**Quick Response (QR) codes**now appear at each section opener, at section-¿level exercises, and as part of the Chapter Tests. Each code links students to the videos and applets that are available for that section, giving them resources at their fingertips.

**Learning Catalytics**helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking.^{™ }

## Table of Contents

**Preface**

**R. Review**- R.1. Success in Mathematics
- R.2. Sets and Classification of Numbers
- R.3. Operations on Signed Numbers; Properties of Real Numbers
- R.4. Order of Operations
- R.5. Algebraic Expressions

**Linear Equations and Inequalities**

### Part I. Linear Equations and Inequalities in One Variable

- 1.1. Linear Equations in One Variable
- 1.2. An Introduction to Problem Solving
- 1.3. Using Formulas to Solve Problems
- 1.4. Linear Inequalities in One Variable
- Putting the Concepts Together (Sections 1.1–1.4)

### Part II. Linear Equations and Inequalities in Two Variables

- 1.5. Rectangular Coordinates and Graphs of Equations
- 1.6. Linear Equations in Two Variables
- 1.7. Parallel and Perpendicular Lines
- 1.8. Linear Inequalities in Two Variables

- Chapter 1 Activity: Pass the Paper
- Chapter 1 Review
- Chapter 1 Test
- Cumulative Review Chapters R–1

**Relations, Functions, and More Inequalities**- 2.1. Relations
- 2.2. An Introduction to Functions
- 2.3. Functions and Their Graphs
- Putting the Concepts Together (Sections 2.1–2.3)

- 2.4. Linear Functions and Models
- 2.5. Compound Inequalities
- 2.6. Absolute Value Equations and Inequalities

- Chapter 2 Activity: Shifting Discovery
- Chapter 2 Review
- Chapter 2 Test

**Systems of Linear Equations and Inequalities**- 3.1. Systems of Linear Equations in Two Variables
- 3.2. Problem Solving: Systems of Two Linear Equations Containing Two Unknowns
- 3.3. Systems of Linear Equations in Three Variables
- Putting the Concepts Together (Sections 3.1–3.3)

- 3.4. Using Matrices to Solve Systems
- 3.5. Determinants and Cramer’s Rule
- 3.6. Systems of Linear Inequalities

- Chapter 3 Activity: Find the Numbers
- Chapter 3 Review
- Chapter 3 Test
- Cumulative Review Chapters R–3
- Getting Ready for Chapter 4: Laws of Exponents and Scientific Notation

**Polynomials and Polynomial Functions**- 4.1. Adding and Subtracting Polynomials
- 4.2. Multiplying Polynomials
- 4.3. Dividing Polynomials; Synthetic Division
- Putting the Concepts Together (Sections 4.1–4.3)

- 4.4. Greatest Common Factor; Factoring by Grouping
- 4.5. Factoring Trinomials
- 4.6. Factoring Special Products
- 4.7. Factoring: A General Strategy
- 4.8. Polynomial Equations

- Chapter 4 Activity: What Is the Question?
- Chapter 4 Review
- Chapter 4 Test
- Getting Ready for Chapter 5: A Review of Operations on Rational Numbers

**Rational Expressions and Rational Functions**- 5.1. Multiplying and Dividing Rational Expressions
- 5.2. Adding and Subtracting Rational Expressions
- 5.3. Complex Rational Expressions
- Putting the Concepts Together (Sections 5.1–5.3)

- 5.4. Rational Equations
- 5.5. Rational Inequalities
- 5.6. Models Involving Rational Expressions
- 5.7. Variation

- Chapter 5 Activity: Correct the Quiz
- Chapter 5 Review
- Chapter 5 Test
- Cumulative Review Chapters R–5
- Getting Ready for Chapter 6: Square Roots

**Radicals and Rational Exponents**- 6.1. nth Roots and Rational Exponents
- 6.2. Simplifying Expressions Using the Laws of Exponents
- 6.3. Simplifying Radical Expressions Using Properties of Radicals
- 6.4. Adding, Subtracting, and Multiplying Radical Expressions
- 6.5. Rationalizing Radical Expressions
- Putting the Concepts Together (Sections 6.1–6.5)

- 6.6. Functions Involving Radicals
- 6.7. Radical Equations and Their Applications
- 6.8. The Complex Number System

- Chapter 6 Activity: Which One Does Not Belong?
- Chapter 6 Review
- Chapter 6 Test

**Quadratic Equations and Functions**- 7.1. Solving Quadratic Equations by Completing the Square
- 7.2. Solving Quadratic Equations by the Quadratic Formula
- 7.3. Solving Equations Quadratic in Form
- Putting the Concepts Together (Sections 7.1–7.3)

- 7.4. Graphing Quadratic Functions Using Transformations
- 7.5. Graphing Quadratic Functions Using Properties
- 7.6. Polynomial Inequalities

- Chapter 7 Activity: Presidential Decision Making
- Chapter 7 Review
- Chapter 7 Test
- Cumulative Review Chapters R–7

**Exponential and Logarithmic Functions**- 8.1. Composite Functions and Inverse Functions
- 8.2. Exponential Functions
- 8.3. Logarithmic Functions
- Putting the Concepts Together (Sections 8.1–8.3)

- 8.4. Properties of Logarithms
- 8.5. Exponential and Logarithmic Equations

- Chapter 8 Activity: Correct the Quiz
- Chapter 8 Review
- Chapter 8 Test

**Conics**- 9.1. Distance and Midpoint Formulas
- 9.2. Circles
- 9.3. Parabolas
- 9.4. Ellipses
- 9.5. Hyperbolas
- Putting the Concepts Together (Sections 9.1–9.5)

- 9.6. Systems of Nonlinear Equations

- Chapter 9 Activity: How Do You Know That . . . ?
- Chapter 9 Review
- Chapter 9 Test
- Cumulative Review: Chapters R–9

**Sequences, Series, and the Binomial Theorem**- 10.1. Sequences
- 10.2. Arithmetic Sequences
- 10.3. Geometric Sequences and Series
- Putting the Concepts Together (Sections 10.1–10.3)

- 10.4. The Binomial Theorem

- Chapter 10 Activity: Discover the Relation
- Chapter 10 Review
- Chapter 10 Test

#### Answers to Selected Exercises

#### Applications Index

#### Subject Index

#### Photo Credits

With training in mathematics, statistics, and economics, **Michael Sullivan III** has a varied teaching background that includes 27 years of instruction in both high school and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series, which he writes with his father, Michael Sullivan.

Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective as to where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series.When not in the classroom or writing, Michael enjoys spending time with his three children, Michael, Kevin, and Marissa, and playing golf. Now that his two sons are getting older, he has the opportunity to do both at the same time!

**Kathy Struve** has been a classroom teacher for nearly 35 years, first at the high school level and, for the past 27 years, at Columbus State Community College. Kathy embraces classroom diversity: diversity of students’ age, learning styles, and previous learning success. She is aware of the challenges of teaching mathematics at a large, urban community college, where students have varied mathematics backgrounds and may enter college with a high level of mathematics anxiety.

Kathy served as Lead Instructor of the Developmental Algebra sequence at Columbus State, where she developed curriculum, conducted workshops, and provided leadership to adjunct faculty in the mathematics department. She embraces the use of technology in instruction, and has taught web and hybrid classes in addition to traditional face-to-face emporium-style classes. She is always looking for ways to more fully involve students in the learning process. In her spare time Kathy enjoys spending time with her two adult daughters, her four granddaughters, and biking, hiking, and traveling with her husband.

Born and raised in San Diego county, **Janet Mazzarella** spent her career teaching in culturally and economically diverse high schools before taking a position at Southwestern College 25 years ago. Janet has taught a wide range of mathematics courses from arithmetic through calculus for math/science/engineering majors and has training in mathematics, education, engineering, and accounting.

Janet has worked to incorporate technology into the curriculum by participating in the development of Interactive Math and Math Pro. At Southwestern College, she helped develop the self-paced developmental mathematics program. In addition, Janet was the Dean of the School of Mathematics, Science, and Engineering, the Chair of the Mathematics Department, the faculty union president, and the faculty coordinator for Intermediate Algebra. In the past, free time consisted of racing motorcycles off-road in the Baja 500 and rock climbing, but recently she has given up the adrenaline rush of these activities for the thrill of traveling in Europe.

**Jessica Bernards and Wendy Fresh of Portland Community College** have worked extensively with the author team to create the How to exercises, new Geogebra applet exercises, and have made the assignments for the New MyMathLab courses.

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