Student Solutions Manual for Intermediate Algebra

Description

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.

Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks where she earned a bachelor’s degree in Secondary Mathematics Education. She has two master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri—Rolla, the second in Adult Education from the University of Missouri—St. Louis. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding. She is able to pursue these interests as a contributor on the Lial Developmental Math series, and a co-author on the Precalculus series.

Student Solutions Manual

Provides completely worked-out solutions to the odd-numbered section exercises and to all exercises in the Now Trys, Relating Concepts, Chapter Reviews, Mixed Review, Chapter Tests, and Cumulative Reviews.

Balancing skills and concepts for the developmental student

• A teacherly writing style walks students through key points of understanding with the aim of readability for the developmental math student.
• Examples with pointers provide tips from the authors for on-the-spot notes and cautions about common pitfalls.
• Now Try Exercises are included as a parallel margin exercise for each numbered example. These exercises immediately apply and reinforce the concepts and skills presented in corresponding examples.
• Comprehensive exercise sets balance students’ procedural skills with conceptual understanding to provide the optimal practice experience to master the topics. In this revision, the conceptual exercises in particular have been increased to ensure that students’ understanding goes beyond rote procedures.
• Expanded – Concept Check exercises have been increased in this revision. These exercises facilitate students’ conceptual understanding at the start of exercise sets, and often emphasize new vocabulary. 
• A type of Concept Check exercise, What Went Wrong exercises, have more than doubled in this revision. These ask students to determine an error in a worked problem, to ensure that they understand common mistakes and realize why those errors are incorrect. Identifying and correcting a mistake requires a higher level of critical thinking.
• Expanded – Relating Concepts exercises have been increased in the revision. Relating Concepts exercise sets tie the topics together and highlight the relationships among various concepts and skills. They work well for individual or group work. These are assignable in MyLab Math.
• Summary exercises are carefully placed in every chapter to provide students with the all-important mixed review problems they need to master topics. Summaries of solution methods or additional examples are often included.
• Additional exercises types include Extending Skills exercises, applications, matching, and fill-in-the-blank problems, all with the aim of arming students with a solid understanding of skills and concepts.
• End of chapter material offers ample opportunity for review. At the end of every chapter, students will find Key Terms and Symbols, Quick Review summaries, Chapter Review exercises, and the all-important Mixed Review. They can also assess their understanding with a Chapter Test and Cumulative Review to retain what they’ve learned thus far.  
• Test Your Word Power exercises in each Chapter Summary help students master mathematical vocabulary, so often a hurdle at this level. 
• Chapter Tests include a fully worked out video solution for every exercise in the Chapter Test.

Resources to support any classroom

• Updated – The extensive video program is updated to be as current as possible:
• An updated section lecture program covers every section of the text. The majority of these videos have been re-filmed for the revision for a visually modern presentation sty. 
• Additionally, shorter solution clip videos, Chapter Test Prep videos, and Quick Review section summary videos are part of the Lial video program, providing a video type for any need.
• No matter how an instructor wants to use or recommend videos for their course, there’s an option that will work for what they or their students need, and all videos include both English and Spanish closed captioning and can be played on mobile devices.
• A Guided Notebook helps students develop organized notes as they work through the course, establishing a good habit while also emphasizing the importance of writing and keeping mathematical work. The Guided Notebook includes Guided Examples with Now Try exercises, extra practice, and key vocabulary terms with vocab practice, for every section from the text.

Options for underprepared students

• To ensure students are caught up on prior skills, every Lial MyLab course now includes Integrated Review.
• Integrated Review provides embedded and personalized review of prerequisite topics within relevant chapters. Students can check their prerequisite skills, and receive personalized practice on the topics they need to focus on, with study aids like worksheets and videos also available to help. 
• Integrated Review assignments – including a Skills Check and personalized homework for the review topics – are premade and available to assign in the Assignment Manager. The review homework includes videos and worksheets as learning aids for relevant exercises to give students remediation right where they need it. 
• Integrated Review can support a corequisite course model, or any course where students would benefit from review. 
• New – Learning Catalytics questions have been premade for every section of the text, giving instructors an easy starting point to take advantage of this learning tool. Premade questions for each section, noted in blue in the Annotated Instructor’s Edition margins, cover prerequisite skills students should be caught up on before starting the section. Learning Catalytics, available through MyLab Math, is an interactive, student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking. 
• Updated – Study Skills support has been moved up to the front of each text in this revision. These short activities provide helpful information, tips, and strategies on a variety of essential skills, and include ways for students to try out the strategy on their own. Study Skills Reminders throughout the text bring students’ attention to these study skills strategies to ensure that students incorporate these strategies all semester.
• New – Skill Builder assignments in MyLab Math 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.
• New – A Mindset module is available in the course, with growth mindset-focused videos and exercises that encourage students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as a learning opportunity.

Also available with MyLab Math 

MyLab™ Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

Teach your course your way

• Flexible platform – Your course is unique. Whether you’d like to build your own assignments, structure students’ work with a learning path, or set prerequisites, you have the flexibility to easily create your course to fit your needs.
• Preparedness – Options for addressing student preparedness include Integrated Review content, Learning Catalytics questions, and study skills materials.

Empower each learner

• Personalized learning – Options to personalize learning with MyLab Math include personalized homework, where a students’ assignments are personalized based on a quiz or test, and Skill Builder assignments which provide in-assignment remediation. 
• Motivation – Engage students using their own devices with new Learning Catalytics questions, available through MyLab Math, that check students’ prerequisite skills for each section in a low-stakes engaging way.

Deliver trusted content

• Author-specific MyLab content – Every exercise in the MyLab is created based on the Lial texts, ensuring that students have a consistent experience. Other resources in the MyLab, such as the videos, are created for the Lial program specifically, to infuse the authors’ approach into the course.
• Conceptual understanding – Expanded Relating Concepts and Concept Check exercises in the text are assignable in MyLab Math to encourage students to connect ideas and see the bigger picture.

Study Skills

• Study Skill 1: Using Your Math Text
• Study Skill 2: Reading Your Math Text
• Study Skill 3: Taking Lecture Notes
• Study Skill 4: Completing Your Homework
• Study Skill 5: Using Study Cards
• Study Skill 6: Managing Your Time
• Study Skill 7: Reviewing a Chapter
• Study Skill 8: Taking Math Tests
• Study Skill 9: Analyzing Your Test Results
• Study Skill 10: Preparing for Your Math Final

1. Review of the Real Number System
   • R.1 Fractions, Decimals, and Percents
   • R.2 Basic Concepts from Algebra
   • R.3 Operations on Real Numbers
   • R.3 Exponents, Roots, and Order of Operations
   • R.4 Properties of Real Numbers
   • Chapter R Summary
   • Chapter R Test
2. Linear Equations, Inequalities, and Applications
   • 1.1 Linear Equations in One Variable
   • 1.2 Formulas and Percent
   • 1.3 Applications of Linear Equations
   • 1.4 Further Applications of Linear Equations
     • Summary Exercises: Applying Problem-Solving Techniques
   • 1.5 Linear Inequalities in One Variable
   • 1.6 Set Operations and Compound Inequalities
   • 1.7 Absolute Value Equations and Inequalities
   • Summary Exercises: Solving Linear and Absolute Value Equations and Inequalities
   • Chapter 1 Summary
   • Chapter 1 Review Exercises
   • Chapter 1 Mixed Review Exercises
   • Chapter 1 Test
   • Chapters R and 1 Cumulative Review Exercises
3. Linear Equations, Graphs, and Functions
   • 2.1 Linear Equations in Two Variables
     • Study Skills: Managing Your Time
   • 2.2 The Slope of a Line
   • 2.3 Writing Equations of Lines
     • Summary Exercises: Finding Slopes and Equations of Lines
   • 2.4 Linear Inequalities in Two Variables
   • 2.5 Introduction to Relations and Functions
   • 2.6 Function Notation and Linear Functions
   • Chapter 2 Summary
   • Chapter 2 Review Exercises
   • Chapter 2 Mixed Review Exercises
   • Chapter 2 Test
   • Chapters R–2 Cumulative Review Exercises
4. Systems of Linear Equations
   • 3.1 Systems of Linear Equations in Two Variables
   • 3.2 Systems of Linear Equations in Three Variables
   • 3.3 Applications of Systems of Linear Equations
   • Chapter 3 Summary
   • Chapter 3 Review Exercises
   • Chapter 3 Mixed Review Exercises
   • Chapter 3 Test
   • Chapters R–3 Cumulative Review Exercises
5. Exponents, Polynomials, and Polynomial Functions
   • 4.1 Integer Exponents
   • 4.2 Scientific Notation
   • 4.3 Adding and Subtracting Polynomials
   • 4.4 Polynomial Functions, Graphs, and Composition
   • 4.5 Multiplying Polynomials
   • 4.6 Dividing Polynomials
   • Chapter 4 Summary
   • Chapter 4 Review Exercises
   • Chapter 4 Mixed Review Exercises
   • Chapter 4 Test
   • Chapters R–4 Cumulative Review Exercises
6. Factoring
   • 5.1 Greatest Common Factors and Factoring by Grouping
   • 5.2 Factoring Trinomials
   • 5.3 Special Factoring
   • 5.4 A General Approach to Factoring
   • 5.5 Solving Equations by the Zero-Factor Property
   • Chapter 5 Summary
   • Chapter 5 Review Exercises
   • Chapter 5 Mixed Review Exercises
   • Chapter 5 Test
   • Chapters R–5 Cumulative Review Exercises
7. Rational Expressions and Functions
   • 6.1 Rational Expressions and Functions; Multiplying and Dividing
   • 6.2 Adding and Subtracting Rational Expressions
   • 6.3 Complex Fractions
   • 6.4 Equations with Rational Expressions and Graphs
     • Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations
   • 6.5 Applications of Rational Expressions
   • 6.6 Variation
   • Chapter 6 Summary
   • Chapter 6 Review Exercises
   • Chapter 6 Mixed Review Exercises
   • Chapter 6 Test
   • Chapters R–6 Cumulative Review Exercises
8. Roots, Radicals, and Root Functions
   • 7.1 Radical Expressions and Graphs
   • 7.2 Rational Exponents
   • 7.3 Simplifying Radicals, the Distance Formula, and Circles
   • 7.4 Adding and Subtracting Radical Expressions
   • 7.5 Multiplying and Dividing Radical Expressions
     • Summary Exercises: Performing Operations with Radicals and Rational Exponents
   • 7.6 Solving Equations with Radicals
   • 7.7 Complex Numbers
   • Chapter 7 Summary
   • Chapter 7 Review Exercises
   • Chapter 7 Mixed Review Exercises
   • Chapter 7 Test
   • Chapters R–7 Cumulative Review Exercises
9. Quadratic Equations, Inequalities, and Functions
   • 8.1 The Square Root Property and Completing the Square
   • 8.2 The Quadratic Formula
   • 8.3 Equations That Lead to Quadratic Methods
     • Summary Exercises: Applying Methods for Solving Quadratic Equations
   • 8.4 Formulas and Further Applications
   • 8.5 Graphs of Quadratic Functions
   • 8.6 More about Parabolas and Their Applications
   • 8.7 Polynomial and Rational Inequalities
   • Chapter 8 Summary
   • Chapter 8 Review Exercises
   • Chapter 8 Mixed Review Exercises
   • Chapter 8 Test
   • Chapters R–8 Cumulative Review Exercises
10. Inverse, Exponential, and Logarithmic Functions
    • 9.1 Inverse Functions
    • 9.2 Exponential Functions
    • 9.3 Logarithmic Functions
    • 9.4 Properties of Logarithms
    • 9.5 Common and Natural Logarithms
    • 9.6 Exponential and Logarithmic Equations; Further Applications
    • Chapter 9 Summary
    • Chapter 9 Review Exercises
    • Chapter 9 Mixed Review Exercises
    • Chapter 9 Test
    • Chapters R–9 Cumulative Review Exercises
11. Nonlinear Functions, Conic Sections, and Nonlinear Systems
    • 10.1 Additional Graphs of Functions
    • 10.2 Circles Revisited and Ellipses
    • 10.3 Hyperbolas and Functions Defined by Radicals
    • 10.4 Nonlinear Systems of Equations
    • 10.5 Second-Degree Inequalities and Systems of Inequalities
    • Chapter 10 Summary
    • Chapter 10 Review Exercises
    • Chapter 10 Mixed Review Exercises
    • Chapter 10 Test
    • Chapters R-10 Cumulative Review Exercises
12. Further Topics in Algebra
    • 11.1 Sequences and Series
    • 11.2 Arithmetic Sequences
    • 11.3 Geometric Sequences
    • 11.4 The Binomial Theorem
    • Chapter 11 Summary
    • Chapter 11 Review Exercises
    • Chapter 11 Mixed Review Exercises
    • Chapter 11 Test
    • Chapters R-11 Cumulative Review Exercises

Appendix A: Synthetic Division

Answers to Selected Exercises

Credits

Index

Updated and expanded features in the text provide students with resources for preparedness and conceptual understanding. 

• Relating Concepts exercises have been increased in the revision. Relating Concepts exercise setstie the topics together and highlight the relationships among various concepts and skills. They work well for individual or group work. These are assignable in MyLab Math.
• What Went Wrong exercises have more than doubled in this revision. These ask students to determine an error in a worked problem, to ensure that they understand common mistakes and realize why those errors are incorrect. Identifying and correcting a mistake requires a higher level of critical thinking.
• Study Skills support has been moved up to the front of each text in this revision. These short activities provide helpful information, tips, and strategies on a variety of essential skills, and include ways for students to try out the strategy on their own. Study Skills Reminders throughout the text bring students’ attention to these study skills strategies to ensure that students incorporate these strategies all semester.

Also available with MyLab Math 

• Increased conceptual questions in the text, including Relating Concepts and What Went Wrong exercises, are assignable in MyLab Math. 

• The extensive video program is updated to be as current as possible:
• A revised section lecture program covers every section of the text, and the majority of these videos have been re-filmed for a more visually appealing and modern presentation style. 
• Additionally, shorter solution clip videos, Chapter Test Prep videos, and Quick Review section summary videos are part of the Lial video program, providing a video type for any need! 
• No matter how an instructor wants to use or recommend videos for their course, there’s an option that will work for what they or their students need, and all videos include both English and Spanish closed captioning and can be played on mobile devices.
• New Learning Catalytics questions have been premade for every section of the text, giving instructors an easy starting point to take advantage of this learning tool. Premade questions for each section, noted in blue in the Annotated Instructor’s Edition margins, cover prerequisite skills students should be caught up on before starting the section. Learning Catalytics, available through MyLab Math, is an interactive, student response tool that uses students’ smartphones, tablets, or laptops to engage them in more sophisticated tasks and thinking. 
• New Skill Builder assignments in MyLab Math 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 new Mindset module is available in the course, with growth mindset-focused videos and exercises that encourage students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as a learning opportunity.

Additional information

Dimensions	1.30 × 8.30 × 10.70 in
Imprint	Pearson
Format	gen
ISBN-13	09780134896359
ISBN-10	0134896351
Author	John Hornsby, Margaret L. Lial, Terry McGinnis
Subjects	mathematics, higher education, Developmental Math, Intermediate Algebra