# Beginning & Intermediate Algebra, 8th edition

Published by Pearson (April 1, 2024) © 2025

**Margaret L. Lial**American River College**John Hornsby**University of New Orleans**Terry McGinnis****Callie J. Daniels**St. Charles Community College

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## MyLab

- Reach every student with personalized support
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For courses in Beginning & Intermediate Algebra (Combined courses).

### A balance of skills and concepts

Part of the Lial Developmental Algebra Series, **Beginning & Intermediate Algebra** uses a clear writing style and a careful blend of skills development and conceptual questions to meet the unique needs of students in this course. The author team retains the hallmark writing style, trusted features and resources that optimize student preparedness and conceptual understanding.

The **8th Edition** updates exercise sets and real-world data; adds new figures, graphs, and diagrams; expands review material; and adds new resources to support conceptual understanding.

### Hallmark features of this title

**Now Try Exercises**next to each example apply and reinforce the concepts and skills presented.**Comprehensive exercise sets**balance students' procedural skills with conceptual understanding.**Concept Check exercises**facilitate students' conceptual understanding at the start of homework.**Relating Concepts exercises**tie the topics together and highlight the relationships among various concepts and skills.**What Went Wrong exercises**ask students to determine an error in a worked problem, to ensure that they understand common mistakes and why those errors are incorrect. Identifying a mistake requires a higher level of critical thinking.

**End-of-chapter material**offers ample opportunity for review, including the all-important Mixed Review, and Test Your Word Power exercises to master vocabulary.

### New and updated features of this title

**NEW/UPDATED: New and updated real-data applications**throughout keep students interested. New applications include social media, streaming services, global issues, gaming, and college expenses. Over 220 examples and exercises use new and updated data.**REVISED: Revised exposition**refines and improves discussions and presentations of topics to increase readability and student understanding.**REVISED: Revised Classroom Exercises and Now Try Exercises**: These trusted features have been carefully evaluated and revised as needed to better match their related section examples. New problems have also been added.**REVISED**:**Enhanced pedagogical use of color**enhances concept development, emphasizes important steps, or highlights key procedures.**NEW: Over 40 new figures and graphs**enhance discussions of topics.

### Features of MyLab Math for the 8th Edition

**REVISED: Nearly half of the section lecture videos have been updated, redone, and filmed by new co-author Callie Daniels**. Full section lecture videos are also available as shorter objective-level videos, along with solution clips and Chapter Test Prep videos.**Quick Review videos**are brief, 5-minute section summaries that recap each section.**NEW: Gradable GeoGebra exercises**enable students to interact directly with the graph in a manner that reflects how students would graph on paper.**NEW: New Setup & Solve Exercises**require students to first describe how they will set up and approach the problem, helping to increase conceptual understanding.**Integrated Review assignments**provide just-in-time review of prerequisite topics within relevant chapters. Prebuilt assignments check what topics students need a refresh on, and videos and worksheets are available to help remediate.**Learning Catalytics**questions have been premade for every section of the text and cover prerequisite skills. Learning Catalytics is an interactive student response tool that uses students' own devices to engage them, gauge understanding in real-time, and facilitate groupwork.**Guided Notebook with Integrated Review**(available for download within MyLab Math or to purchase separately) helps students keep their work organized as they work through their course. It includes Learning Objectives, Key Vocabulary Terms and Practice, Guided Examples, Now Try Exercises, and extra practice exercises,

### 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

### R. Prealgebra Review

- R.1 Fractions
- R.2 Decimals and Percents

### 1. The Real Number System

- 1.1 Exponents, Order of Operations, and Inequality
- 1.2 Variables, Expressions, and Equations
- 1.3 Real Numbers and the Number Line
- 1.4 Adding and Subtracting Real Numbers
- 1.5 Multiplying and Dividing Real Numbers
- Summary Exercises: Performing Operations with Real Numbers
- 1.6 Properties of Real Numbers
- 1.7 Simplifying Expressions
- Chapter 1 Summary
- Chapter 1 Review Exercises
- Chapter 1 Mixed Review Exercises
- Chapter 1 Test
- Chapters R and 1 Cumulative Review Exercises

### 2. Linear Equations and Inequalities in One Variable

- 2.1 The Addition Property of Equality
- 2.2 The Multiplication Property of Equality
- 2.3 Solving Linear Equations Using Both Properties of Equality
- 2.4 Clearing Fractions and Decimals When Solving Linear Equations
- Summary Exercises: Applying Methods for Solving Linear Equations
- 2.5 Applications of Linear Equations
- 2.6 Formulas and Additional Applications from Geometry
- 2.7 Ratio, Proportion, and Percent
- 2.8 Further Applications of Linear Equations
- 2.9 Solving Linear Inequalities
- Chapter 2 Summary
- Chapter 2 Review Exercises
- Chapter 2 Mixed Review Exercises
- Chapter 2 Test
- Chapters R - 2 Cumulative Review Exercises

### 3. Linear Equations in Two Variables

- 3.1 Linear Equations and Rectangular Coordinates
- 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
- Chapter 3 Summary
- Chapter 3 Review Exercises
- Chapter 3 Mixed Review Exercises
- Chapter 3 Test
- Chapters R - 3 Cumulative Review Exercises

### 4. Exponents and Polynomials

- 4.1 The Product Rule and Power Rules for Exponents
- 4.2 Integer Exponents and the Quotient Rule
- Summary Exercises: Applying the Rules for Exponents
- 4.3 Scientific Notation
- 4.4 Adding, Subtracting, and Graphing Polynomials
- 4.5 Multiplying Polynomials
- 4.6 Special Products
- 4.7 Dividing Polynomials
- Chapter 4 Summary
- Chapter 4 Review Exercises
- Chapter 4 Mixed Review Exercises
- Chapter 4 Test
- Chapters R - 4 Cumulative Review Exercises

### 5. Factoring and Applications

- 5.1 Greatest Common Factor; Factoring by Grouping
- 5.2 Factoring Trinomials
- 5.3 More on Factoring Trinomials
- 5.4 Special Factoring Techniques
- Summary Exercises: Recognizing and Applying Factoring Strategies
- 5.5 Solving Quadratic Equations Using the Zero-Factor Property
- 5.6 Applications of Quadratic Equations
- Chapter 5 Summary
- Chapter 5 Review Exercises
- Chapter 5 Mixed Review Exercises
- Chapter 5 Test
- Chapters R - 5 Cumulative Review Exercises

### 6. Rational Expressions and Applications

- 6.1 The Fundamental Property of Rational Expressions
- 6.2 Multiplying and Dividing Rational Expressions
- 6.3 Least Common Denominators
- 6.4 Adding and Subtracting Rational Expressions
- 6.5 Complex Fractions
- 6.6 Solving Equations with Rational Expressions
- Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations
- 6.7 Applications of Rational Expressions
- Chapter 6 Summary
- Chapter 6 Review Exercises
- Chapter 6 Mixed Review Exercises
- Chapter 6 Test
- Chapters R - 6 Cumulative Review Exercises

### 7. Linear Equations, Graphs, and Systems

- 7.1 Review of Graphs and Slopes of Lines
- 7.2 Review of Equations of Lines; Linear Models
- 7.3 Solving Systems of Linear Equations by Graphing
- 7.4 Solving Systems of Linear Equations by Substitution
- 7.5 Solving Systems of Linear Equations by Elimination
- Summary Exercises: Applying Techniques for Solving Systems of Linear Equations
- 7.6 Systems of Linear Equations in Three Variables
- 7.7 Applications of Systems of Linear Equations
- Chapter 7 Summary
- Chapter 7 Review Exercises
- Chapter 7 Mixed Review Exercises
- Chapter 7 Test
- Chapters R - 7 Cumulative Review Exercises

### 8. Inequalities and Absolute Value

- 8.1 Review of Linear 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 Linear Inequalities and Systems in Two Variables
- Chapter 8 Summary
- Chapter 8 Review Exercises
- Chapter 8 Mixed Review Exercises
- Chapter 8 Test
- Chapters R - 8 Cumulative Review Exercises

### 9. Relations and Functions

- 9.1 Introduction to Relations and Functions
- 9.2 Function Notation and Linear Functions
- 9.3 Polynomial Functions, Operations, and Composition
- 9.4 Variation
- Chapter 9 Summary
- Chapter 9 Review Exercises
- Chapter 9 Mixed Review Exercises
- Chapter 9 Test
- Chapters R - 9 Cumulative Review Exercises

### 10. Roots, Radicals, and Root Functions

- 10.1 Radical Expressions and Graphs
- 10.2 Rational Exponents
- 10.3 Simplifying Radicals, the Distance Formula, and Circles
- 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
- Chapter 10 Summary
- Chapter 10 Review Exercises
- Chapter 10 Mixed Review Exercises
- Chapter 10 Test
- Chapters R - 10 Cumulative Review Exercises

### 11. 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 That Lead to Quadratic Methods
- 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
- Chapter 11 Summary
- Chapter 11 Review Exercises
- Chapter 11 Mixed Review Exercises
- Chapter 11 Test
- Chapters R - 11 Cumulative Review Exercises

### 12. Inverse, Exponential, and Logarithmic Functions

- 12.1 Inverse Functions
- 12.2 Exponential Functions
- 12.3 Logarithmic Functions
- 12.4 Properties of Logarithms
- 12.5 Common and Natural Logarithms
- 12.6 Exponential and Logarithmic Equations; Further Applications
- Chapter 12 Summary
- Chapter 12 Review Exercises
- Chapter 12 Mixed Review Exercises
- Chapter 12 Test
- Chapters R - 12 Cumulative Review Exercises

### 13. Nonlinear Functions, Conic Sections, and Nonlinear Systems

- 13.1 Additional Graphs of Functions
- 13.2 Circles Revisited 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
- Chapter 13 Summary
- Chapter 13 Review Exercises
- Chapter 13 Mixed Review Exercises
- Chapter 13 Test
- Chapters R - 13 Cumulative Review Exercises

### 14. Further Topics in Algebra

- 14.1 Sequences and Series
- 14.2 Arithmetic Sequences
- 14.3 Geometric Sequences
- 14.4 The Binomial Theorem
- Chapter 14 Summary
- Chapter 14 Review Exercises
- Chapter 14 Mixed Review Exercises
- Chapter 14 Test
- Chapters R - 14 Cumulative Review Exercises

### About our authors

The late **Marge Lial **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 25 years of teaching at the high school and university levels and 15 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 2 sons, Andrew and Tyler.

**Callie Daniels **has taught mathematics at St. Charles Community College for 30 years. She has served as Faculty Association President and Math Department Chair, and has taught a variety of courses in traditional, hybrid and online formats. She holds a Master of Science Degree in Applied Mathematics and Statistics from the Missouri University of Science and Technology, a master's degree in Adult Education from the University of Missouri-St. Louis, and a bachelor's degree in Secondary Mathematics Education from the University of the Ozarks. During her time at the University of the Ozarks, she played 3 college sports and was an Academic All-American. Callie's teaching interests include motivating students to achieve their potential, finding new ways to use technology to help students learn, and providing support materials for faculty.

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