Study Skill 1: Using Your Math TextStudy Skill 2: Reading Your Math TextStudy Skill 3: Taking Lecture NotesStudy Skill 4: Completing Your HomeworkStudy Skill 5: Using Study CardsStudy Skill 6: Managing Your TimeStudy Skill 7: Reviewing a ChapterStudy Skill 8: Taking Math TestsStudy Skill 9: Analyzing Your Test ResultsStudy Skill 10: Preparing for Your Math Final R. Prealgebra Review R.1 FractionsR.2 Decimals and Percents 1. The Real Number System 1.1 Exponents, Order of Operations, and Inequality1.2 Variables, Expressions, and Equations1.3 Real Numbers and the Number Line1.4 Adding and Subtracting Real Numbers1.5 Multiplying and Dividing Real NumbersSummary Exercises: Performing Operations with Real Numbers1.6 Properties of Real Numbers1.7 Simplifying ExpressionsChapter 1 SummaryChapter 1 Review ExercisesChapter 1 Mixed Review ExercisesChapter 1 TestChapters R and 1 Cumulative Review Exercises 2. Linear Equations and Inequalities in One Variable 2.1 The Addition Property of Equality2.2 The Multiplication Property of Equality2.3 Solving Linear Equations Using Both Properties of Equality2.4 Clearing Fractions and Decimals When Solving Linear EquationsSummary Exercises: Applying Methods for Solving Linear Equations2.5 Applications of Linear Equations2.6 Formulas and Additional Applications from Geometry2.7 Ratio, Proportion, and Percent2.8 Further Applications of Linear Equations2.9 Solving Linear InequalitiesChapter 2 SummaryChapter 2 Review ExercisesChapter 2 Mixed Review ExercisesChapter 2 TestChapters R-2 Cumulative Review Exercises 3. Linear Equations in Two Variables 3.1 Linear Equations and Rectangular Coordinates3.2 Graphing Linear Equations in Two Variables3.3 The Slope of a Line3.4 Slope-Intercept Form of a Linear Equation3.5 Point-Slope Form of a Linear Equation and ModelingSummary Exercises: Applying Graphing and Equation-Writing Techniques for LinesChapter 3 SummaryChapter 3 Review ExercisesChapter 3 Mixed Review ExercisesChapter 3 TestChapters R-3 Cumulative Review Exercises 4. Exponents and Polynomials 4.1 The Product Rule and Power Rules for Exponents4.2 Integer Exponents and the Quotient RuleSummary Exercises: Applying the Rules for Exponents4.3 Scientific Notation4.4 Adding, Subtracting, and Graphing Polynomials4.5 Multiplying Polynomials4.6 Special Products4.7 Dividing PolynomialsChapter 4 SummaryChapter 4 Review ExercisesChapter 4 Mixed Review ExercisesChapter 4 TestChapters R-4 Cumulative Review Exercises 5. Factoring and Applications 5.1 Greatest Common Factor; Factoring by Grouping5.2 Factoring Trinomials5.3 More on Factoring Trinomials5.4 Special Factoring TechniquesSummary Exercises: Recognizing and Applying Factoring Strategies5.5 Solving Quadratic Equations Using the Zero-Factor Property5.6 Applications of Quadratic EquationsChapter 5 SummaryChapter 5 Review ExercisesChapter 5 Mixed Review ExercisesChapter 5 TestChapters R-5 Cumulative Review Exercises 6. Rational Expressions and Applications 6.1 The Fundamental Property of Rational Expressions6.2 Multiplying and Dividing Rational Expressions6.3 Least Common Denominators6.4 Adding and Subtracting Rational Expressions6.5 Complex Fractions6.6 Solving Equations with Rational ExpressionsSummary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations6.7 Applications of Rational ExpressionsChapter 6 SummaryChapter 6 Review ExercisesChapter 6 Mixed Review ExercisesChapter 6 TestChapters R-6 Cumulative Review Exercises 7. Linear Equations, Graphs, and Systems 7.1 Review of Graphs and Slopes of Lines7.2 Review of Equations of Lines; Linear Models7.3 Solving Systems of Linear Equations by Graphing7.4 Solving Systems of Linear Equations by Substitution7.5 Solving Systems of Linear Equations by EliminationSummary Exercises: Applying Techniques for Solving Systems of Linear Equations7.6 Systems of Linear Equations in Three Variables7.7 Applications of Systems of Linear EquationsChapter 7 SummaryChapter 7 Review ExercisesChapter 7 Mixed Review ExercisesChapter 7 TestChapters R-7 Cumulative Review Exercises 8. Inequalities and Absolute Value 8.1 Review of Linear Inequalities in One Variable8.2 Set Operations and Compound Inequalities8.3 Absolute Value Equations and InequalitiesSummary Exercises: Solving Linear and Absolute Value Equations and Inequalities8.4 Linear Inequalities and Systems in Two VariablesChapter 8 SummaryChapter 8 Review ExercisesChapter 8 Mixed Review ExercisesChapter 8 TestChapters R-8 Cumulative Review Exercises 9. Relations and Functions 9.1 Introduction to Relations and Functions9.2 Function Notation and Linear Functions9.3 Polynomial Functions, Operations, and Composition9.4 VariationChapter 9 SummaryChapter 9 Review ExercisesChapter 9 Mixed Review ExercisesChapter 9 TestChapters R-9 Cumulative Review Exercises 10. Roots, Radicals, and Root Functions 10.1 Radical Expressions and Graphs10.2 Rational Exponents10.3 Simplifying Radicals, the Distance Formula, and Circles10.4 Adding and Subtracting Radical Expressions10.5 Multiplying and Dividing Radical ExpressionsSummary Exercises: Performing Operations with Radicals and Rational Exponents10.6 Solving Equations with Radicals10.7 Complex NumbersChapter 10 SummaryChapter 10 Review ExercisesChapter 10 Mixed Review ExercisesChapter 10 TestChapters R-10 Cumulative Review Exercises 11. Quadratic Equations, Inequalities, and Functions 11.1 Solving Quadratic Equations by the Square Root Property11.2 Solving Quadratic Equations by Completing the Square11.3 Solving Quadratic Equations by the Quadratic Formula11.4 Equations That Lead to Quadratic MethodsSummary Exercises: Applying Methods for Solving Quadratic Equations11.5 Formulas and Further Applications11.6 Graphs of Quadratic Functions11.7 More about Parabolas and Their Applications11.8 Polynomial and Rational InequalitiesChapter 11 SummaryChapter 11 Review ExercisesChapter 11 Mixed Review ExercisesChapter 11 TestChapters R-11 Cumulative Review Exercises 12. Inverse, Exponential, and Logarithmic Functions 12.1 Inverse Functions12.2 Exponential Functions12.3 Logarithmic Functions12.4 Properties of Logarithms12.5 Common and Natural Logarithms12.6 Exponential and Logarithmic Equations; Further ApplicationsChapter 12 SummaryChapter 12 Review ExercisesChapter 12 Mixed Review ExercisesChapter 12 TestChapters R-12 Cumulative Review Exercises 13. Nonlinear Functions, Conic Sections, and Nonlinear Systems 13.1 Additional Graphs of Functions13.2 Circles Revisited and Ellipses13.3 Hyperbolas and Functions Defined by Radicals13.4 Nonlinear Systems of Equations13.5 Second-Degree Inequalities and Systems of InequalitiesChapter 13 SummaryChapter 13 Review ExercisesChapter 13 Mixed Review ExercisesChapter 13 TestChapters R-13 Cumulative Review Exercises 14. Further Topics in Algebra 14.1 Sequences and Series14.2 Arithmetic Sequences14.3 Geometric Sequences14.4 The Binomial TheoremChapter 14 SummaryChapter 14 Review ExercisesChapter 14 Mixed Review ExercisesChapter 14 TestChapters R-14 Cumulative Review Exercises

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.

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.