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Preface

Preface

Elementary Algebra was originally authored by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, and published by OpenStax, Rice University. It is licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). The original work is available at openstax.org. This version has been adapted for use in the Universal Open Textbook Initiative.

About Elementary Algebra

Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

Coverage and Scope

Elementary Algebra follows a nontraditional approach in its presentation of content. Building on the content in Prealgebra, the material is presented as a sequence of small steps so that students gain confidence in their ability to succeed in the course. The order of topics was carefully planned to emphasize the logical progression through the course and to facilitate a thorough understanding of each concept. As new ideas are presented, they are explicitly related to previous topics.

  • Chapter 1: Foundations
     Chapter 1 reviews arithmetic operations with whole numbers, integers, fractions, and decimals, to give the student a solid base that will support their study of algebra.
  • Chapter 2: Solving Linear Equations and Inequalities
     In Chapter 2, students learn to verify a solution of an equation, solve equations using the Subtraction and Addition Properties of Equality, solve equations using the Multiplication and Division Properties of Equality, solve equations with variables and constants on both sides, use a general strategy to solve linear equations, solve equations with fractions or decimals, solve a formula for a specific variable, and solve linear inequalities.
  • Chapter 3: Math Models
     Once students have learned the skills needed to solve equations, they apply these skills in Chapter 3 to solve word and number problems.
  • Chapter 4: Graphs
     Chapter 4 covers the rectangular coordinate system, which is the basis for most consumer graphs. Students learn to plot points on a rectangular coordinate system, graph linear equations in two variables, graph with intercepts, understand slope of a line, use the slope-intercept form of an equation of a line, find the equation of a line, and create graphs of linear inequalities.
  • Chapter 5: Systems of Linear Equations
     Chapter 5 covers solving systems of equations by graphing, substitution, and elimination; solving applications with systems of equations, solving mixture applications with systems of equations, and graphing systems of linear inequalities.
  • Chapter 6: Polynomials
     In Chapter 6, students learn how to add and subtract polynomials, use multiplication properties of exponents, multiply polynomials, use special products, divide monomials and polynomials, and understand integer exponents and scientific notation.
  • Chapter 7: Factoring
     In Chapter 7, students explore the process of factoring expressions and see how factoring is used to solve certain types of equations.
  • Chapter 8: Rational Expressions and Equations
     In Chapter 8, students work with rational expressions, solve rational equations, and use them to solve problems in a variety of applications.
  • Chapter 9: Roots and Radical
     In Chapter 9, students are introduced to and learn to apply the properties of square roots, and extend these concepts to higher order roots and rational exponents.
  • Chapter 10: Quadratic Equations
     In Chapter 10, students study the properties of quadratic equations, solve and graph them. They also learn how to apply them as models of various situations.

All chapters are broken down into multiple sections, the titles of which can be viewed in the Table of Contents.

Key Features and Boxes

Examples

Each learning objective is supported by one or more worked examples that demonstrate the problem-solving approaches that students must master. Typically, we include multiple Examples for each learning objective to model different approaches to the same type of problem, or to introduce similar problems of increasing complexity.

All Examples follow a simple two- or three-part format. First, we pose a problem or question. Next, we demonstrate the solution, spelling out the steps along the way. Finally (for select Examples), we show students how to check the solution. Most Examples are written in a two-column format, with explanation on the left and math on the right to mimic the way that instructors "talk through" examples as they write on the board in class.

Be Prepared!

Each section, beginning with Section 2.1, starts with a few "Be Prepared!" exercises so that students can determine if they have mastered the prerequisite skills for the section. Reference is made to specific Examples from previous sections so students who need further review can easily find explanations. Answers to these exercises can be found in the supplemental resources that accompany this title.

Try It
A dark grey right-pointing chevron symbol is centered within a white square, framed by a soft, light blue gradient border. This icon typically represents 'next,' 'forward,' or 'expand'.

A "Try It" exercise immediately follows an Example, providing the student with an immediate opportunity to solve a similar problem. In the PDF and the Web View version of the text, answers to the Try It exercises are located in the Answer Key.

How To
An avatar of a person with a neutral expression, next to a speech bubble containing three ellipses, suggesting thought, a pending response, or a message being typed.

How To feature typically follows the Try It exercises and outlines the series of steps for how to solve the problem in the preceding Example.

Media
A teal-colored play button icon, depicted as a right-pointing triangle, centered within a white square with a soft, blurred teal border. It signifies the start of video or audio playback.

The "Media" icon appears at the conclusion of each section, just prior to the Section Exercises. This icon marks a list of links to online video tutorials that reinforce the concepts and skills introduced in the section.

Self Check The Self Check includes the learning objectives for the section so that students can self-assess their mastery and make concrete plans to improve.

Art Program

Elementary Algebra contains many figures and illustrations. Art throughout the text adheres to a clear, understated style, drawing the eye to the most important information in each figure while minimizing visual distractions.

This figure shows three x y-coordinate planes. The first plane shows two lines which intersect at one point. Under the graph it says,

Section Exercises

Each section of every chapter concludes with a well-rounded set of exercises that can be assigned as homework or used selectively for guided practice. Exercise sets are named Practice Makes Perfect to encourage completion of homework assignments.

  • Exercises correlate to the learning objectives. This facilitates assignment of personalized study plans based on individual student needs.
  • Exercises are carefully sequenced to promote building of skills.
  • Values for constants and coefficients were chosen to practice and reinforce arithmetic facts.
  • Even and odd-numbered exercises are paired.
  • Exercises parallel and extend the text examples and use the same instructions as the examples to help students easily recognize the connection.
  • Applications are drawn from many everyday experiences, as well as those traditionally found in college math texts.
  • Everyday Math highlights practical situations using the concepts from that particular section
  • Writing Exercises are included in every exercise set to encourage conceptual understanding, critical thinking, and literacy.

Chapter Review Features

Each chapter concludes with a review of the most important takeaways, as well as additional practice problems that students can use to prepare for exams.

  • Key Terms provide a formal definition for each bold-faced term in the chapter.
  • Key Concepts summarize the most important ideas introduced in each section, linking back to the relevant Example(s) in case students need to review.
  • Chapter Review Exercises include practice problems that recall the most important concepts from each section.
  • Practice Test includes additional problems assessing the most important learning objectives from the chapter.
  • Answer Key includes the answers to all Try It exercises and every other exercise from the Section Exercises, Chapter Review Exercises, and Practice Test.

Answers to Questions in the Book

Answers to Examples are provided just below the question in the book. All Try It answers are provided in the Answer Key. Odd-numbered Section Exercises, Chapter Review Exercises, and Practice Test questions are provided to students in the Answer Key. Even-numbered answers are provided only to instructors in the Instructor Answer Guide via the Instructor Resources page.

Additional Resources

Instructor resources for this book include manipulative mathematics worksheets, an answer key to Be Prepared Exercises, and a Getting Started Guide. These are available through the OpenStax instructor resources page for this book. Instructors can also find and share community-created teaching materials at oercommons.org/hubs/OpenStax.

About the Authors

Senior Contributing Authors

Lynn Marecek and MaryAnne Anthony-Smith have been teaching mathematics at Santa Ana College for many years and have worked together on several projects aimed at improving student learning in developmental math courses. They are the authors of Strategies for Success: Study Skills for the College Math Student, published by Pearson HigherEd.

Lynn Marecek, Santa Ana College

MaryAnne Anthony-Smith, Santa Ana College

Andrea Honeycutt Mathis, Northeast Mississippi Community College

Reviewers

Jay Abramson, Arizona State University
 Bryan Blount, Kentucky Wesleyan College
 Gale Burtch, Ivy Tech Community College
 Tamara Carter, Texas A&M University
 Danny Clarke, Truckee Meadows Community College
 Michael Cohen, Hofstra University
 Christina Cornejo, Erie Community College
 Denise Cutler, Bay de Noc Community College
 Lance Hemlow, Raritan Valley Community College
 John Kalliongis, Saint Louis Iniversity
 Stephanie Krehl, Mid-South Community College
 Laurie Lindstrom, Bay de Noc Community College
 Beverly Mackie, Lone Star College System
 Allen Miller, Northeast Lakeview College
 Christian Roldán-Johnson, College of Lake County Community College
 Martha Sandoval-Martinez, Santa Ana College
 Gowribalan Vamadeva, University of Cincinnati Blue Ash College
 Kim Watts, North Lake College
 Libby Watts, Tidewater Community College
 Allen Wolmer, Atlantic Jewish Academy
 John Zarske, Santa Ana College