The manual provides detailed solutions to the odd-numbered section-level exercises and to all margin, Relating Concepts, Summary, Chapter Review, Chapter Test, and Cumulative Review Exercises.
About the Book
Student-friendly features to make math accessible
- Margin Problems allow students to immediately practice the example material and check their answer at the bottom of the page in preparation for the exercise sets.
- Real-Life Applications with interesting data are used in many new or updated examples and exercises throughout the text. Students are often asked to find data in a table, chart, graph, or advertisement. These applied problems provide an up-to-date flavor that will appeal to and motivate students.
- Learning Objectives begin each section, and all material is keyed to these objectives to let students and instructors know exactly what will be covered.
- Pointers within examples, Cautions (highlighted in yellow) and Notes (highlighted in blue) provide students with important, on-the-spot reminders and warnings about common pitfalls. Expanded! A popular feature, Pointers have been increased in this edition.
- UPDATED! Study Skills activities provide students with proven strategies for learning math. Many of these now include a Now Try This section to increase student involvement and accountability for the study skills activities.
- Vocabulary Tips in the margins of the first few chapters help students learn root words and prefixes.
- The new and engaging Chapter Openers portray real-life situations that make math relevant for students.
- Figures and Photos provide visual learners with a presentation of mathematical figures, diagrams, tables, and graphs whenever possible and use a style similar to that seen by students in today’s print and electronic media.
- Calculator Tips are optional tips, marked with a red calculator icon, that offer helpful information and instruction for students using calculators in the course.
Pedagogy that develops conceptual understanding alongside skill development
- Concept Checks at the start of exercise sets ensure students have the skills to proceed, and later help students consolidate learning by writing, correcting errors, and practicing processes.
- EXPANDED! Some Concept Checks include What Went Wrong Exercises, which have been expanded in this revision. Earlier editions of the text included exercises designed to help students find and fix errors, but in this edition these exercises have been updated and expanded with explicit instructions to emphasize the importance of this aspect of the learning process. When students can find and correct errors, they are demonstrating a higher level of understanding and conceptual knowledge.
- UPDATED! Relating Concepts exercises, located at the end of many section exercise sets, help students tie concepts together and develop higher-level problem-solving skills as they compare and contrast ideas, identify and describe patterns, and extend concepts to new situations. These exercises make great collaborative activities for pairs or small groups of students. Many more of these problem types have been included in the revision, and all Relating Concepts exercises are now assignable in the MyLab™ Math course, noted with an “RC”.
- EXPANDED! Guided Solution exercises, noted with a “GS” in the margin and exercise sets, show the first steps of the solution process, providing guidance to students as they start learning a new concept or procedure. These exercises encourage understanding of the problem solving process, rather than completing the steps by rote, and also keep students on the right track as they work through the problem-so
New to this Edition
About the Book
- Study Skills activities provide students with proven strategies for learning math. Many of these now include a Now Try This section to increase student involvement and accountability for the study skills activities.
- Relating Concepts exercises, located at the end of many section exercise sets, help students tie concepts together and develop higher-level problem-solving skills as they compare and contrast ideas, identify and describe patterns, and extend concepts to new situations. These exercises make great collaborative activities for pairs or small groups of students. Many more of these problem types have been included in the revision, and all Relating Concepts exercises are now assignable in the MyLab™ Math course, noted with an “RC”.
- Guided Solution exercises, noted with a “GS” in the margin and exercise sets, show the first steps of the solution process, providing guidance to students as they start learning a new concept or procedure. These exercises encourage understanding of the problem solving process, rather than completing the steps by rote, and also keep students on the right track as they work through the problem-solving steps. Many of the Guided Solutions exercises in the end of section sets are assignable in MyLab Math, and utilize a ‘guided’ functionality in the program. Coverage of these exercises in MyLab Math has been increased in this revision.
- Examples and exercises have been adjusted or replaced with current data. Applications put math in context to motivate students and were updated to cover a wider variety of topics, including technology, ecology, and health sciences. The variety of end-of-section exercise sets provide students with opportunities to practice, apply, connect, and extend the skills they are learning.
- In addition to Chapter Review exercises keyed to sections from the chapter, Chapter Reviews include a full page of dedicated Mixed Review exercises, to help students synthesize concepts.
Specific content changes include the following:
- Exercise sets have been updated with a renewed focus on conceptual understanding, skill development, and review. New or revised figures are included wherever possible.
- Real-world data in the examples and exercises has been updated.
- More “word equations” are included in application examples to help students translate words into equations.
- Expanded Chapter R includes new figures and exposition on fractions, as well as new discussion, examples, and exercises on converting between fractions, decimals, and percents.
- Expanded MidChapter
- Summary Exercises in Chapter 2 continue our emphasis on the difference between simplifying expressions and solving equations. The mid-chapter
- Summary Exercises in Chapters 4, 6, 7, and 11 include new examples that illustrate and distinguish between solution methods.
- Separate sections on slope-intercept form and point-slope form now appear in Chapter 3 and include enhanced discussion and new examples and exercises.
- Reorganized Chapter 5 introduces the rules for exponents and application to scientific notation at the beginning of the chapter, followed by the sections on polynomials and their operations.
- Expanded Chapter 7 on rational expressions introduces the material in more sections that now include additional examples and exercise. Emphasis I s given to recognizing equivalent forms of rational expressions.
- Chapter 8, which revisits topics from the first half of the course, includes new Section 8.4 that reviews graphing linear equations in two variables and slope.
- New Chapter 9 now includes the material on functions, function notation, linear functions, and variation. New Section 9.3 introduces polynomial function, graphs, and operations. Each subsequent chapter in the text presents a new class of functions.
- The following topics are among those that have been enhanced and/or expanded:
- Operations with signed numbers (Sections 1.4—1.6)
- Order of operations involving absolute value expressions (Sections 1.5 and 1.6)
- Solving linear equations in one variable (Sections 2.1 and 2.2)
- Solving linear inequalities with fractions (Section 2.7)
- Graphing linear equations in two variables using intercepts (Section 3.2)
- Solving linear systems of equations using elimination (Section 4.3)
- Dividing a polynomial by a polynomial (Section 5.7)
- Discussion of sums of squares and factoring perfect square trinomials (Section 6.5)
- General Factoring strategies (Section 6.6)
- Solving systems of linear equations in there variables (Section 8.6)
- Multiplying radical expressions (Section 10.5)
- Solving quadratic equations by completing the square (Section 11.2)
- Solving quadratic inequalities (Section 11.7)
- Finding and graphing inverse functions (Section 12.2)
- Graphing systems of linear inequalities (Section 13.5)
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.
- New exercise types and functionality give instructors an abundance of choice for assignment creation, and ensure that students’ practice in their MyLab Math course gives them a well-rounded understanding of concepts and procedures.
- Guided Solution Exercises are assignable in MyLab Math. These exercises are noted with a GS icon in the section exercise sets, and a GS notation in the Assignment Manager. Coverage of Guided Solution exercises has been increased in this revision. These exercises allow instructors to assess student understanding of the problem-solving process, rather than completing the steps by rote, and to also keep students on the right track as they work through the problem-solving steps.
- Relating Concepts exercises in the text help students make connections and problem-solve at a higher level. These sets are assignable in MyLab Math, with expanded coverage in this revision.
- 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.
- Skill Builder assignments offer 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.
- A variety of resources bring the hallmark Lial pedagogy and approach into the MyLab Math course.
- The extensive Lial video program makes the MyLab Math course a true learning environment, and gives students support right when they need it, wherever they need it. The variety of videos give instructors flexibility - different types of videos allow for different learning environments, such as a flipped classroom or lab, and different assignment types. Many of the videos have been updated in this revision to more closely match the exercises from the text, in a more modern presentation format. Videos available include the following, which all offer optional English and Spanish captioning:
- Solutions Clips for select exercises marked with a Play Button icon in the text and eText show an instructor working through the complete solution to that exact problem.
- Objective-level videos are short, bite-size chunks taken from the section lecture videos. Students often will not watch a video longer than 5 minutes, so objective-level videos give just the right amount of content to keep their attention.
- Section Lecture Videos are available for every section, and offer a navigation menu by example and objective.
- Quick Review Lectures provide a summary of key concepts for each chapter.
- Chapter Test Prep Videos show solutions for all Chapter Test exercises. They can also be accessed on YouTube.
- The Lial Video Workbook corresponds to the videos, and gives students a place to record the examples from the videos and try problems on their own.
- 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.
- In addition to a library of premade developmental math questions in Learning Catalytics, the authors have included suggested Learning Catalytics questions, drawing on prerequisite skills, at the start of each section to check student preparedness for the new material. These questions are available as annotations in the Annotated Instructor Edition - check out the Instructor Resources tab in MyLab Math to learn more.
- In addition to assignable Study Skills and Reading Connection material, new Mindset material has been added to the course. This content encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as a learning opportunity - so often a major hurdle for developmental math students.
- Accessibility enhancements continue Pearson’s commitment to make products accessible to as many students as possible. This latest course release is compatible with the JAWS screen reader, enabling print-disabled students to access and interact with numerous problems as noted by an icon within the assignment manager. The course also works with the ZoomText enlarger, and includes an HTML eBook that is compatible with JAWS and other Windows screen readers, allowing all students to access the same text, at the same place, and at the same price. Additionally, all videos include subtitles.
Table of Contents
Table of Contents
- R. Prealgebra Review
- R.1 Fractions
- R.2 Decimals and Percents
- Study Skills Using Your Math Text
- The Real Number System
- 1.1 Exponents, Order of Operations, and Inequality
- Study Skills Taking Lecture Notes
- 1.2 Variables, Expressions, and Equations
- Study Skills Reading Your Math Text
- 1.3 Real Numbers and the Number Line
- Study Skills Using Study Cards
- 1.4 Adding Real Numbers
- 1.5 Subtracting Real Numbers
- Study Skills Completing Your Homework
- 1.6 Multiplying and Dividing Real Numbers
- Summary Exercises Performing Operations with Real Numbers
- 1.7 Properties of Real Numbers
- 1.8 Simplifying Expressions
- Study Skills Reviewing a Chapter
- Equations, Inequalities, and Applications
- 2.1 The Addition Property of Equality
- Study Skills Managing Your Time
- 2.2 The Multiplication Property of Equality
- 2.3 More on Solving Linear Equations
- Study Skills Using Study Cards Revisited
- Summary Exercises Applying Methods for Solving Linear Equations
- 2.4 An Introduction to Applications of Linear Equations
- 2.5 Formulas and Additional Applications from Geometry
- 2.6 Ratio, Proportion, and Percent
- Summary Exercises Applying Problem-Solving Techniques
- 2.7 Solving Linear Inequalities
- Study Skills Taking Math Tests
- Graphs of Linear Equations and Inequalities in Two Variables
- 3.1 Linear Equations and Rectangular Coordinates
- Study Skills Analyzing Your Test Results
- 3.2 Graphing Linear Equations in Two Variables
- 3.3 The Slope of a Line
- 3.4 Slope-Intercept Form of a Linear Equation
- 3.5 Point-Slope Form of a Linear Equation and Modeling
- Summary Exercises Applying Graphing and
- Equation-Writing Techniques for Lines
- Study Skills Preparing for Your Math Final Exam
- 3.6 Graphing Linear Inequalities in Two Variables
- 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 Elimination
- Summary Exercises Applying Techniques for Solving Systems of Linear Equations
- 4.4 Applications of Linear Systems
- 4.5 Solving Systems of Linear Inequalities
- Exponents and Polynomials
- 5.1 The Product Rule and Power Rules for Exponents
- 5.2 Integer Exponents and the Quotient Rule
- Summary Exercises Applying the Rules for Exponents
- 5.3 An Application of Exponents: Scientific Notation
- 5.4 Adding and Subtracting Polynomials
- 5.5 Multiplying Polynomials
- 5.6 Special Products
- 5.7 Dividing a Polynomial by a Monomial
- 5.8 Dividing a Polynomial by a Polynomial
- Factoring and Applications
- 6.1 Greatest Common Factors; Factor by Grouping
- 6.2 Factoring Trinomials
- 6.3 Factoring Trinomials by Grouping
- 6.4 Factoring Trinomials Using the FOIL Method
- 6.5 Special Factoring Techniques
- 6.6 A General Approach to Factoring
- 6.7 Solving Quadratic Equations Using the Zero-Factor Property
- 6.8 Applications of Quadratic Equations
- Rational Expressions and Applications
- 7.1 The Fundamental Property of Rational Expressions
- 7.2 Multiplying and Dividing Rational Expressions
- 7.3 Least Common Denominators
- 7.4 Adding and Subtracting Rational Expressions
- 7.5 Complex Fractions
- 7.6 Solving Equations with Rational Expressions
- Summary Exercises Simplifying Rational Expressions vs. Solving Rational Equations
- 7.7 Applications of Rational Expressions
- 7.8 Variation
- Equations, Inequalities, Graphs, and Systems Revisited
- 8.1 Review of Solving Linear Equations and Inequalities in one Variable
- 8.2 Set Operations and Compound Inequalities
- 8.3 Absolute Value Equations and Inequalities
- Summary Exercises Solving Linear and Absolute Value Equations and Inequalities
- 8.4 Review of Graphing Linear Equations in Two Variables; Slope
- 8.6 Systems of Linear Equations in Three Variables; Applications
- Relations and Functions
- 9.1 Introduction to Relations and Functions
- 9.2 Function Notation and Linear Functions
- 9.3 Polynomial Functions, Operations, and Graphs
- 9.4 Variation
- Roots, Radicals, and Root Functions
- 10.1 Radical Expressions and Graphs
- 10.2 Rational Exponents
- 10.3 Simplifying Radical Expressions
- 10.4 Adding and Subtracting Radical Expressions
- 10.5 Multiplying and Dividing Radical Expressions
- Summary Exercises Performing Operations with Radicals and Rational Exponents
- 10.6 Solving Equations with Radicals
- 10.7 Complex Numbers
- Quadratic Equations, Inequalities, and Functions
- 11.1 Solving Quadratic Equations by the Square Root Property
- 11.2 Solving Quadratic Equations by Completing the Square
- 11.3 Solving Quadratic Equations by the Quadratic Formula
- 11.4 Equations Quadratic in Form
- Summary Exercises Applying Methods for Solving Quadratic Equations
- 11.5 Formulas and Further Applications
- 11.6 Graphs of Quadratic Functions
- 11.7 More about Parabolas and Their Applications
- 11.8 Polynomial and Rational Inequalities
- Inverse, Exponential, and Logarithmic Functions
- 12.1 Composition of Functions
- 12.2 Inverse Functions
- 12.3 Exponential Functions
- 12.4 Logarithmic Functions
- 12.5 Properties of Logarithms
- 12.6 Common and Natural Logarithms
- 12.7 Exponential and Logarithmic Equations and Their Applications
- Nonlinear Functions, Conic Sections, and Nonlinear Systems
- 13.1 Additional Graphs of Functions
- 13.2 Circles and Ellipses
- 13.3 Hyperbolas and Functions Defined by Radicals
- 13.4 Nonlinear Systems of Equations
- 13.5 Second-Degree Inequalities and Systems of Inequalities
Appendix A: Review of Exponents, Polynomials, and Factoring (Transition from Introductory to Intermediate Algebra)
Appendix B: Synthetic Division
Appendix C: Solving Systems of Linear Equations by Matrix Methods
Answers to Selected Exercises
Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh), and has been an avid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.
A native Midwesterner, Terry McGinnis received her Bachelor's of Science in Elementary Education with a concentration in Mathematics from Iowa State University. She has taught elementary and middle school mathematics, and developed and implemented the curriculum used with her students. Terry has been involved in college mathematics publishing for over 20 years, working with a variety of authors on textbooks in both developmental mathematics and precalculus. After working behind the scenes on many of the Lial/Hornsby textbooks and supplements for over 10 years, Terry joined Margaret Lial and John Hornsby in 2002 as coauthor of their developmental mathematics series. When not working, Terry enjoys spinning at a local health club, walking, and reading fiction. She is the devoted mother of two sons, Andrew and Tyler.