## Overview

#### Description

For courses in Beginning & Intermediate Algebra.

This package includes MyLab Math.

Understanding and Applying Mathematical Concepts

The goal of the ** Bittinger Concepts and Applications Series** is to help today’s student learn and retain mathematical concepts. This proven program prepares students for the transition from skills-oriented elementary algebra courses to more concept-oriented college-level mathematics courses. This requires the development of critical-thinking skills: to reason mathematically, to communicate mathematically, and to identify and solve mathematical problems. The new editions support students with a tightly integrated MyLab™ Math course; a strong focus on problem-solving, applications, and concepts, and the robust MyMathGuide workbook and objective-based video program. In addition, new material—developed as a result of the authors’ experience in the classroom, as well as from insights from faculty and students—includes more systematic review and preparation for practice, as well as stronger focus on real-world applications.

Personalize learning 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.

NOTE: This text requires a title-specific MyLab Math access kit** .** The title-specific access kit provides access to the Bittinger/Ellenbogen/Johnson,

*accompanying MyLab course ONLY.*

**Elementary & Intermediate Algebra: Concepts & Applications 7/e**#### This product accompanies

## Features

**Personalize learning 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.

NOTE: This text requires a title-specific MyLab Math access kit** .** The title-specific access kit provides access to the Bittinger/Ellenbogen/Johnson,

*accompanying MyLab course ONLY.*

**Elementary & Intermediate Algebra: Concepts & Applications 7/e**

**Prepare and motivate students with resources that support personalized learning and conceptual understanding**

**NEW! Skill Builder**offers adaptive practice that is designed to increase students’ ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.**NEW! Workspace Assignments**allow students to work through an exercise step-by-step, adjusting to the path each student takes and allowing them to show their mathematical reasoning as they progress, receiving feedback when and where they need it most. When accessed via a mobile device, Workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus.**NEW! Student Success Module**, available in the left-hand navigation of MyLab Math, includes videos, activities, and post-tests for these three student success areas:**Study Skills**, including “Time Management” and “Preparing for and Taking Exams,” and**College Success**, including “College Transition” and “Online Learning.”**Active Learning Figures**are interactive animations available in MyMathLab. They allow students to examine visual representations of concepts through both guided and open-ended exploration to further solidify their understanding of these concepts.is an objective-based workbook (available in print and in MyLab Math) for guided, hands-on learning. It offers vocabulary, skill, and concept review–along with problem-solving practice–with space for students to show their work and write notes. Students can follow along in*MyMathGuide: Notes, Practice, and Video Path**MyMathGuide*while they watch the new To-the-Point Objective Videos, listen to their instructor lecture, or read the textbook.

**Engage and guide students through concepts with a variety of robust multimedia resources**

**ENHANCED! Increased coverage of skill-building, conceptual, and applications exercises**, plus new problem types such as drag & drop, provide even more flexibility when creating homework.**NEW! To-the-Point Objective Videos**is a comprehensive program of objective-based, interactive videos that can be used hand-in-hand with the*MyMathGuide*workbook. Video support for Interactive Your Turn exercises in the videos prompts students to solve problems and receive instant feedback.**NEW! Chapter Opener applications with Infographics**use current data and applications to present the math in context. These applications are linked to exercises in the text and MyLab Math course to help students model, visualize, and learn the math. These openers also feature spotlights on real people sharing how they use math in their careers.**Bittinger Video Program**includes all new To-the-Point Objective Videos and Chapter Test Prep Videos.**Interactive “Your Turn” Exercises**in the videos prompt students to solve problems and receive instant feedback. The videos also can be used hand-in-hand with the new*MyMathGuide*workbook.**NEW! Student Activities**begin with real-world data and guide students to examine a key concept in each chapter, while analyzing the data and connecting other concepts. There is one activity per chapter and they are available in MyLab Math.**EXPANDED! Interactive exercises in**MyLab Math help build problem-solving skills and foster conceptual understanding. For the Seventh Edition, Guided Solutions exercises were added to reinforce the step-by-step problem-solving process, while the new Drag & Drop functionality was applied to matching exercises throughout the course to better assess a student’s understanding of the concepts.**NEW! 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.^{™ }- Upload a full PowerPoint
^{®}deck for easy creation of slide questions. - Team names are no longer case sensitive.
- Help your students develop critical thinking skills.
- Monitor responses to find out where your students are struggling.
- Rely on real-time data to adjust your teaching strategy.
- Automatically group students for discussion, teamwork, and peer-to-peer learning.

**About the Book**

**A GUIDED LEARNING PATH**

To enhance the learning process and improve learner outcomes, the Bittinger program provides a broad range of support for students and instructors. Each person can personalize his or her learning or teaching experience by accessing help when he or she needs it.

**PREPARE: Studying the concepts**

Students can learn about each math concept by reading the textbook or eText, watching the To-the-Point Objective videos, participating in class, working in the *MyMathGuide* workbook – or using whatever combination of these course resources works best for him or her.

**The Bittinger five-step problem-solving process**helps students develop a consistent approach to setting up and solving problems: (1) Familiarize, (2) Translate, (3) Carry out, (4) Check, and (5) State the answer. Repeated use of this problem-solving strategy throughout the text provides students with a starting point for any type of problem they encounter, and frees them to focus on the unique aspects of the particular problem.**UPDATED! The body of the text**has been enhanced to help students better build their skills and understand key underlying concepts. The exposition, examples, and exercises have been carefully reviewed and, as appropriate, revised or replaced. New content includes more systematic review and preparation for practice, as well as stronger focus on the real-world applications for the math.**UPDATED! Interesting, contemporary applications of mathematics**, many of which make use of real data, help motivate students and instructors. In this new edition, the authors have updated real-world data examples and exercises to include subjects such as renewable energy, graduate-school acceptance, and zipline rides.

**PARTICIPATE: Making connections through active exploration**

Knowing that developing a solid grasp of the big picture is a key to student success, the authors offer many opportunities for active learning to help students practice, review, and confirm their understanding of key concepts and skills.

**Exploring the Concept**,**Algebraic-Graphical Connections**, and optional**Technology Connections**encourage students to think about and visualize concepts.**Connecting the Concepts**summarize several sections, and are followed by**Mixed Review exercises**, to help students understand how concepts work together.**Student Notes**and**Study Skills**are strategically located throughout the text.**Chapter Resources**are additional learning materials compiled at the end of each chapter, making them easy to integrate into the course at the most appropriate time. The mathematics necessary to use the resource has been presented by the end of the section indicated with each resource.**Translating for Success and Visualizing for Success.**These are matching exercises that help students learn to translate word problems to mathematical language and to graph equations and inequalities.**Collaborative Activity.**Students who work in groups generally outperform those who do not, so these optional activities direct them to explore mathematics together. Additional collaborative activities and suggestions for directing collaborative learning appear in the Instructor’s Resources Manual with Tests and Mini Lectures.**Decision Making: Connection.**Although many applications throughout the text involve decision- making situations, this feature specifically applies the math of each chapter to a context in which students may be involved in decision making.

**PRACTICE: Reinforcing understanding**

As students explore the math, they have frequent opportunities to practice, self-assess, and reinforce their understanding.

**Your Turn exercises**appear after every example and direct students to work similar problems for immediate reinforcement of skills and concepts.**NEW! Check Your Understanding**offers students the chance to reflect on the concepts just discussed before beginning the exercise set. Working problems and answering questions helps students focus on the key skills and concepts just learned.**Mid-Chapter Reviews**offer guided solutions and mixed review exercises.**Study Summary**gives a synopsis of key terms and concepts which are paired with worked-out examples and practice exercises.**Chapter Review and Test**provides a thorough chapter review and practice test.**Cumulative Review**helps students retain and apply their knowledge from previous chapters.

**EXERCISE SETS**

**Vocabulary and Reading Check exercises**begin every exercise set.**Concept Reinforcement exercises**appearing near the beginning of exercise sets, build students’ comprehension through True/False, matching, and fill-in-the-blank exercises.**Aha! exercises**are designed to encourage students to “look before they leap," and they can be solved quickly without lengthy computation, if the student has the proper insight.**Skill Review exercises**review all major concepts covered previously, and often focus on a single topic from multiple perspectives. To solve the**Synthesis exercises**that follow, students will often need to use skills and concepts from earlier sections. This will help them develop deeper insight into the current topic.**Writing exercises**appear just before the Skill Review exercises, and they aid comprehension by requiring students to use critical thinking to explain concepts in one or more complete sentences.**Quick Quiz**at the end of exercise sets provides ongoing chapter review and help students prepare for te chapter test.**Prepare to Move On**at the end of exercise sets reviews previously covered skills and concepts to prepare students for the next section.**Chapter Resources**are compiled at the end of each chapter to make it easy to integrate into the course at the most appropriate time. They include:**Decision Making: Connections**to prepare students for math use in day-to-day life, along with**Translating for Success**,**Visualizing for Success**, and**Collaborative Activities**.

### New to This Edition

**Personalize learning 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.

NOTE: This text requires a title-specific MyLab Math access kit** .** The title-specific access kit provides access to the Bittinger/Ellenbogen/Johnson,

*accompanying MyLab course ONLY.*

**Elementary & Intermediate Algebra: Concepts & Applications 7/e**

**Prepare and motivate students with resources that support personalized learning and conceptual understanding**

**Skill Builder**offers adaptive practice that is designed to increase students’ ability to complete their assignments. By monitoring student performance on their homework, Skill Builder adapts to each student’s needs and provides just-in-time, in-assignment practice to help them improve their proficiency of key learning objectives.**Workspace Assignments**allow students to work through an exercise step-by-step, adjusting to the path each student takes and allowing them to show their mathematical reasoning as they progress, receiving feedback when and where they need it most. When accessed via a mobile device, Workspace exercises use handwriting recognition software that allows students to naturally write out their answers with their fingertip or stylus.**Student Success Module**, available in the left-hand navigation of MyLab Math, includes videos, activities, and post-tests for these three student success areas:

**Engage and guide students through concepts with a variety of robust multimedia resources**

**Increased coverage of skill-building, conceptual, and applications exercises**, plus new problem types such as drag & drop, provide even more flexibility when creating homework.**To-the-Point Objective Videos**is a comprehensive program of objective-based, interactive videos that can be used hand-in-hand with the*MyMathGuide*workbook. Video support for Interactive Your Turn exercises in the videos prompts students to solve problems and receive instant feedback.**Chapter Opener applications with Infographics**use current data and applications to present the math in context. These applications are linked to exercises in the text and MyLab Math course to help students model, visualize, and learn the math. These openers also feature spotlights on real people sharing how they use math in their careers.**Student Activities**begin with real-world data and guide students to examine a key concept in each chapter, while analyzing the data and connecting other concepts. There is one activity per chapter and they are available in MyLab Math.**Expanded Interactive exercises in**MyLab Math help build problem-solving skills and foster conceptual understanding. For the Seventh Edition, Guided Solutions exercises were added to reinforce the step-by-step problem-solving process, while the new Drag & Drop functionality was applied to matching exercises throughout the course to better assess a student’s understanding of the concepts.**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.^{™ }- Upload a full PowerPoint
^{®}deck for easy creation of slide questions. - Team names are no longer case sensitive.
- Help your students develop critical thinking skills.
- Monitor responses to find out where your students are struggling.
- Rely on real-time data to adjust your teaching strategy.
- Automatically group students for discussion, teamwork, and peer-to-peer learning.

**About the Book**

**A GUIDED LEARNING PATH**

To enhance the learning process and improve learner outcomes, the Bittinger program provides a broad range of support for students and instructors. Each person can personalize his or her learning or teaching experience by accessing help when he or she needs it.

**PREPARE: Studying the concepts**

Students can learn about each math concept by reading the textbook or etext, watching the To-the-Point Objective videos, participating in class, working in the *MyMathGuide* workbook – or using whatever combination of these course resources works best for him or her.

**The body of the text**has been enhanced to help students better build their skills and understand key underlying concepts. The exposition, examples, and exercises have been carefully reviewed and, as appropriate, revised or replaced. New content includes more systematic review and preparation for practice, as well as stronger focus on the real-world applications for the math.**Updated, interesting, and contemporary applications of mathematics**, many of which make use of real data, help motivate students and instructors. In this new edition, the authors have updated real-world data examples and exercises to include subjects such as renewable energy, graduate-school acceptance, and zipline rides

**PRACTICE: Reinforcing understanding**

As students explore the math, they have frequent opportunities to practice, self-assess, and reinforce their understanding.

**Check Your Understanding**offers students the chance to reflect on the concepts just discussed before beginning the exercise set. Working problems and answering questions helps students focus on the key skills and concepts just learned.

## Table of Contents

1. Introduction to Algebraic Expressions

1.1 Introduction to Algebra

1.2 The Commutative, Associative, and Distributive Laws

1.3 Fraction Notation

1.4 Positive and Negative Real Numbers

1.5 Addition of Real Numbers

1.6 Subtraction of Real Numbers

1.7 Multiplication and Division of Real Numbers

1.8 Exponential Notation and Order of Operations

2. Equations, Inequalities, and Problem Solving

2.1 Solving Equations

2.2 Using the Principles Together

2.3 Formulas

2.4 Applications with Percent

2.5 Problem Solving

2.6 Solving Inequalities

2.7 Solving Applications with Inequalities

3. Introduction to Graphing

3.1 Reading Graphs, Plotting Points, and Scaling Graphs

3.2 Graphing Linear Equations

3.3 Graphing and Intercepts

3.4 Rates

3.5 Slope

3.6 Slope-Intercept Form

3.7 Point—Slope Form and Equations of Lines

4. Polynomials

4.1 Exponents and Their Properties

4.2 Negative Exponents and Scientific Notation

4.3 Polynomials

4.4 Addition and Subtraction of Polynomials

4.5 Multiplication of Polynomials

4.6 Special Products

4.7 Polynomials in Several Variables

4.8 Division of Polynomials

5. Polynomials and Factoring

5.1 Introduction to Factoring

5.2 Factoring Trinomials of the Type x^{2}+bx+c

5.3 Factoring Trinomials of the Type ax^{2}+bx+c

5.4 Factoring Perfect-Square Trinomials and Differences of Squares

5.5 Factoring Sums or Differences of Cubes

5.6 Factoring: A General Strategy

5.7 Solving Quadratic Equations by Factoring

5.8 Solving Applications

6. Rational Expression and Equations

6.1 Rational Expressions

6.2 Multiplication and Division

6.3 Addition, Subtraction, and Least Common Denominators

6.4 Addition and Subtraction with Unlike Denominators

6.5 Complex Rational Expressions

6.6 Rational Equations

6.7 Applications Using Rational Equations and Proportions

7. Functions and Graphs

7.1 Introduction to Functions

7.2 Domain and Range

7.3 Graphs of Functions

7.4 The Algebra of Functions

7.5 Formulas, Applications, and Variation

8. Systems of Linear Equations and Problem Solving

8.1 Systems of Equations in Two Variables

8.2 Solving by Substitution or Elimination

8.3 Solving Applications: Systems of Two Equations

8.4 Systems of Equations in Three Variables

8.5 Solving Applications: Systems of Three Equations

8.6 Elimination Using Matrices

8.7 Determinants and Cramer’s Rule

8.8 Business and Economics Applications

9. Inequalities and Problem Solving

9.1 Inequalities and Applications

9.2 Intersections, Unions, and Compound Inequalities

9.3 Absolute-Value Equations and Inequalities

9.4 Inequalities in Two Variables

9.5 Applications Using Linear Programming

10. Exponents and Radicals

10.1 Radical Expressions and Functions

10.2 Rational Numbers as Exponents

10.3 Multiplying Radical Expressions

10.4 Dividing Radical Expressions

10.5 Expressions Containing Several Radical Terms

10.6 Solving Radical Equations

10.7 The Distance Formula, the Midpoint Formula, and Other Applications

10.8 The Complex Numbers

11. Quadratic Functions and Equations

11.1 Quadratic Equations

11.2 The Quadratic Formula

11.3 Studying Solutions of Quadratic Equations

11.4 Applications Involving Quadratic Equations

11.5 Equations Reducible to Quadratic

11.6 Quadratic Functions and Their Graphs

11.7 More About Graphing Quadratic Functions

11.8 Problem Solving and Quadratic Functions

11.9 Polynomial Inequalities and Rational Inequalities

12. Exponential Functions and Logarithmic Functions

12.1 Composite Functions and Inverse Functions

12.2 Exponential Functions

12.3 Logarithmic Functions

12.4 Properties of Logarithmic Functions

12.5 Common Logarithms and Natural Logarithms

12.6 Solving Exponential Equations and Logarithmic Equations

12.7 Applications of Exponential Functions and Logarithmic Functions

13. Conic Sections

13.1 Conic Sections: Parabolas and Circles

13.2 Conic Sections: Ellipses

13.3 Conic Sections: Hyperbolas

13.4 Nonlinear Systems of Equations

14. Sequences, Series, and the Binomial Theorem

14.1 Sequences and Series

14.2 Arithmetic Sequences and Series

14.3 Geometric Sequences and Series

14.4 The Binomial Theorem

R. Elementary Algebra Review

R.1 Introduction to Algebraic Expressions

R.2 Equations, Inequalities, and Problem Solving

R.3 Introduction to Graphing

R.4 Polynomials

R.5 Polynomials and Factoring

R6. Rational Expressions and Equations

Appendix A. Mean, Median, and Mode

Appendix B. Sets

Appendix C. Synthetic Division and the Remainder Theorem

## Order

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## About the Author(s)

**Marvin Bittinger **has taught math at the university level for more than thirty-eight years, and he is now professor emeritus of mathematics education at Indiana University-Purdue University. Professor Bittinger has authored numerous textbooks on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

**David Ellenbogen**has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts—Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing, and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.

**Barbara Johnson**has a BS in mathematics from Bob Jones University and a MS in mathematics from Clemson University, and she is currently pursuing a PhD in Educational Studies at Ball state University. She has taught high school and college math for 30 years, and she enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she is also a student of karate.

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