R. Review of the Real Number System R.1 Basic Concepts R.2 Operations on Real Numbers R.3 Exponents, Roots, and Order of Operations R.4 Properties of Real Numbers Study Skills Using Your Math Text Study Skills Reading Your Math Text   1. Linear Equations and Applications 1.1 Linear Equations in One Variable Study Skills Completing Your Homework 1.2 Formulas and Percent Study Skills Managing Your Time 1.3 Applications of Linear Equations Study Skills Taking Lecture Notes 1.4 Further Applications of Linear Equations Summary Exercises Applying Problem-Solving Techniques Study Skills Reviewing a Chapter   2. Linear Inequalities and Absolute Value 2.1 Linear Inequalities in One Variable Study Skills Using Study Cards 2.2 Set Operations and Compound Inequalities Study Skills Using Study Cards Revisited 2.3 Absolute Value Equations and Inequalities Summary Exercises Solving Linear and Absolute Value Equations and Inequalities  Study Skills Taking Math Tests   3. Graphs, Linear Equations and Functions 3.1 The Rectangular Coordinate System Study Skills Analyzing Your Test Results 3.2 Slope of a Line 3.3 Linear Equations in Two Variables Summary Exercises Finding Slopes and Equations of Lines 3.4 Linear Inequalities in Two Variables 3.5 Introduction to Relations and Functions 3.6 Function Notation and Linear Functions   4. Systems of Linear Equations 4.1 Systems of Linear Equations in Two Variables Study Skills Preparing for Your Math Final Exam 4.2 Systems of Linear Equations in Three Variables 4.3 Applications of Systems of Linear Equations   5. Exponents, Polynomials, and Polynomial Functions 5.1 Integer Exponents 5.2 Scientific Notation 5.3 Adding and Subtracting Polynomials 5.4 Polynomial Functions and Graphs 5.5 Multiplying Polynomials 5.6 Dividing Polynomials   6. Factoring 6.1 Greatest Common Factors and Factoring by Grouping 6.2 Factoring Trinomials 6.3 Special Factoring

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. 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. 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.   CONTENT CHANGES 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 have been updated. Sections 1.4, 2.3, and 4.3 include new problem-solving objectives, examples, exercises, and/or hints. Section 1.2 provides new formulas from the health care industry. The presentation on linear equation in two variables in Section 3.1 has been reorganized. New exercises have been added in Sections 3.1–3.3 to make better connections among tables, equations, and graphs of linear equations. The introduction to relations and functions in Section 3.5 has a new example and expanded discussion on relations and ordered pairs. Scientific notation is covered separately in Section 5.2. Increased connections between operations with rational numbers and operations with rational expressions are made in Sections 7.1–7.3. The following topics are among those that have been enhanced and/or expanded: Solving linear equations in one variable with fraction and decimal coefficients (Section 1.1) Graphing linear inequalities in two variables (Section 3.4) Solving systems of linear equations in three variables (Section 4.2) Factoring sums and differences of cubes (Section 6.3) General factoring strategies (Section 6.4) Determining domains of rational functions (Sections 7.1, 7.4) Solving rational equations (Section 7.4) Multiplying radical expressions (Section 8.5) Solving quadratic equations using the zero-factor property and the quadratic formula (Sections 9.1, 9.2) Solving quadratic inequalities (Section 9.7) Finding and graphing inverse functions (Section 10.2) Graphing systems of linear inequalities (Section 11.5) 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.