Complete Solutions Manual Algebra Combined Approach 6th Edition All Chapters Step-by-Step Answers Study Guide 2026

COMPLETE SOLUTIONS MANUAL ALGEBRA A Combined Approach 6th EDITION Step-by-Step Solutions to ALL Problems Detailed Explanations for Every Exercise Verified Answers & Complete Work Shown Perfect for Homework & Exam Prep Learn Problem-Solving Techniques All Chapters Fully Covered Why Students Love This Resource: Save Hours of Work • Ace Your Homework • Understand Concepts Better Check Your Answers • Study Smart • Improve Your Grades HIGH-QUALITY • COMPLETE • READY TO USE • INSTANT ACCESS What's Inside This Solutions Manual Complete Chapter Coverage: Chapter 1: Real Numbers and Algebraic Expressions Chapter 2: Equations, Inequalities, and Problem Solving Chapter 3: Graphs and Functions Chapter 4: Systems of Equations and Inequalities Chapter 5: Exponents, Polynomials, and Functions Chapter 6: Rational Expressions and Equations Chapter 7: Rational Exponents, Radicals, and Functions Chapter 8: Quadratic Equations and Functions Chapter 9: Exponential and Logarithmic Functions Plus: Additional chapters and appendices What Makes This Special: • Every single problem solved with complete work shown • Clear, easy-to-follow explanations for each step • Helps you understand WHY, not just WHAT the answer is • Identify where you went wrong and learn from mistakes • Build confidence for tests and exams • Save time on homework assignments Pro Study Tip: Try solving each problem yourself FIRST, then check your work against the solutions. This way you'll learn the material better and identify your weak areas for focused study. Educational Study Material • Copyright-Free Content • For Academic Use INSTRUCTOR’S SOLUTIONS MANUAL ALGEBRA: A COMBINED APPROACH SIXTH EDITION Elayn Martin-Gay University of New Orleans The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the docu mentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs. Reproduced by Pearson from electronic files supplied by the author. Copyright © 2020, 2016, 2012 by Pearson Education, Inc., 221 River Street, Hoboken, NJ 07030. All rights reserved. Printed in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms and the appropriate contacts within the Pearson Education Global Rights and Permissions Department, please visit ISBN-13: 978-0-13- 522667-4 ISBN-10: 0-13-522667-8 Contents Chapter R Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 1 23 55 118 171 215 259 300 355 388 429 477 583 642 Appendices 699 Practice Final Exam 724 Copyright © 2020 Pearson Education, Inc. 1 Chapter R Section R.1 Practice Exercises 1. 10 = 1 ⋅ 10, 10 = 2 ⋅ 5 The factors of 10 are 1, 2, 5, and 10. 2. 18 = 1 ⋅ 18, 18 = 2 ⋅ 9, 18 = 3 ⋅ 6 The factors of 18 are 1, 2, 3, 6, 9, and 18. 3. 5 is a prime number. Its factors are 1 and 5 only. 16 is a composite number. Its factors are 1, 2, 4, 8, and 16. 23 is a prime number. Its factors are 1 and 23 only. 42 is a composite number. Its factors are 1, 2, 3, 6, 7, 14, 21, and 42. 4. 44 = 4 ⋅ 11 = 2 ⋅ 2 ⋅ 11 The prime factorization of 44 is 2 ⋅ 2 ⋅ 11. 5. 60 = 4 ⋅ 15 = 2 ⋅ 2 ⋅ 3 ⋅ 5 The prime factorization of 60 is 2 ⋅ 2 ⋅ 3 ⋅ 5. 6. 11 3 33 3 99 3297 The prime factorization of 297 is 3 ⋅ 3 ⋅ 3 ⋅ 11. 7. 14 = 2 ⋅ 7 35 = 5 ⋅ 7 LCM = 2 ⋅ 5 ⋅ 7 = 70 8. 5 = 5 9 = 3 ⋅ 3 LCM = 3 ⋅ 3 ⋅ 5 = 45 9. 4 = 2 ⋅ 2 15 = 3 ⋅ 5 10 = 2 ⋅ 5 LCM = 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60 Vocabulary, Readiness & Video Check R.1 1. The number 40 equals 2 ⋅ 2 ⋅ 2 ⋅ 5. Since each factor is prime, we call 2 ⋅ 2 ⋅ 2 ⋅ 5 the prime factorization of 40. 2. A natural number, other than 1, that is not prime is called a composite number. 3. A natural number that has exactly two different factors, 1 and itself, is called a prime number. 4. The least common multiple of a list of numbers is the smallest number that is a multiple of all the numbers in the list. 5. To factor means to write as a product. 6. A multiple of a number is the product of that number and any natural number. 7. No, the natural number 1 is neither prime nor composite. 8. We may write factors in different order, but every natural number has only one prime factorization. 9. The least common multiple, LCM, of a list of numbers is the smallest number that is a multiple of each number in the list. Exercise Set R.1 2. 8 = 1 ⋅ 8, 8 = 2 ⋅ 4 The factors of 8 are 1, 2, 4, and 8. 4. 36 = 1 ⋅ 36, 36 = 2 ⋅ 18, 36 = 3 ⋅ 12, 36 = 4 ⋅ 9, 36 = 6 ⋅ 6 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. 6. 63 = 1 ⋅ 63, 63 = 3 ⋅ 21, 63 = 7 ⋅ 9 The factors of 63 are 1, 3, 7, 9, 21, and 63. 8. 50 = 1 ⋅ 50, 50 = 2 ⋅ 25, 50 = 5 ⋅ 10 The factors of 50 are 1, 2, 5, 10, 25, and 50. 10. 31 = 1 ⋅ 31 The factors of 31 are 1 and 31. 12. 21 is a composite number. Its factors are 1, 3, 7, and 21. 14. 53 is a prime number. Its factors are only 1 and 53. 16. 51 is a composite number. Its factors are 1, 3, 17, and 51. 18. 307 is a prime number. Its factors are only 1 and 307. Chapter R: Prealgebra Review ISM: Algebra A Combined Approach 2 Copyright © 2020 Pearson Education, Inc. 20. 1798 is a composite number. Its factors are 1, 2, 29, 31, 58, 62, 899, and 1798. 22. 28 = 2 ⋅ 14 = 2 ⋅ 2 ⋅ 7 The prime factorization of 28 is 2 ⋅ 2 ⋅ 7. 24. 30 = 2 ⋅ 15 = 2 ⋅ 3 ⋅ 5 The prime factorization of 30 is 2 ⋅ 3 ⋅ 5. 26. 48 224 2212 2226 22223 = ⋅ = ⋅ ⋅ = ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ The prime factorization of 48 is 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3. 28. 64 = 4 ⋅ 4 ⋅ 4 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 The prime factorization of 64 is 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2. 30. 5 5 25 5125 2250 2500 The prime factorization of 500 is 2 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ 5. 32. 7 5 35 3105 3315 The prime factorization of 315 is 3 ⋅ 3 ⋅ 5 ⋅ 7. 34. 63 = 3 ⋅ 21 = 3 ⋅ 3 ⋅ 7 The prime factorization of 63 is 3 ⋅ 3 ⋅ 7, which is choice c. 36. 4 = 2 ⋅ 2 5 = 5 LCM = 2 ⋅ 2 ⋅ 5 = 20 38. 9 = 3 ⋅ 3 15 = 3 ⋅ 5 LCM = 3 ⋅ 3 ⋅ 5 = 45 40. 30 = 2 ⋅ 3 ⋅ 5 40 = 2 ⋅ 2 ⋅ 2 ⋅ 5 LCM = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 5 = 120 42. 2 = 2 11 = 11 LCM = 2 ⋅ 11 = 22 44. 4 = 2 ⋅ 2 18 = 2 ⋅ 3 ⋅ 3 LCM = 2 ⋅ 2 ⋅ 3 ⋅ 3 = 36 46. 18 = 2 ⋅ 3 ⋅ 3 30 = 2 ⋅ 3 ⋅ 5 LCM = 2 ⋅ 3 ⋅ 3 ⋅ 5 = 90 48. 50 = 2 ⋅ 5 ⋅ 5 70 = 2 ⋅ 5 ⋅ 7 LCM = 2 ⋅ 5 ⋅ 5 ⋅ 7 = 350 50. 21 = 3 ⋅ 7 28 = 2 ⋅ 2 ⋅ 7 LCM = 2 ⋅ 2 ⋅ 3 ⋅ 7 = 84 52. 3 = 3 9 = 3 ⋅ 3 20 = 2 ⋅ 2 ⋅ 5 LCM = 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 5 = 180 54. 3 = 3 5 = 5 7 = 7 LCM = 3 ⋅ 5 ⋅ 7 = 105 56. 9 = 3 ⋅ 3 36 = 2 ⋅ 2 ⋅ 3 ⋅ 3 72 = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 LCM = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 = 72 58. 4 = 2 ⋅ 2 14 = 2 ⋅ 7 35 = 5 ⋅ 7 LCM = 2 ⋅ 2 ⋅ 5 ⋅ 7 = 140 60. answers may vary 62. 35 = 5 ⋅ 7 20 = 2 ⋅ 2 ⋅ 5 LCM = 2 ⋅ 2 ⋅ 5 ⋅ 7 = 140 They are in New Orleans on the same day every 140 days. 64. 1000 = 25 ⋅ 40 = 25 ⋅ 5 ⋅ 8 1125 = 25 ⋅ 45 = 25 ⋅ 5 ⋅ 9 LCM = 25 ⋅ 5 ⋅ 8 ⋅ 9 = 9000 Section R.2 Practice Exercises 1. 4 1 4= since 4 ÷ 4 = 1. ISM: Algebra A Combined Approach Chapter R: Prealgebra Review Copyright © 2020 Pearson Education, Inc. 3 2. 9 3 3= since 9 ÷ 3 = 3. 3. 10 1 10= since 10 ÷ 10 = 1. 4. 5 5 1= since 5 ÷ 1 = 5. 5. 0 0 11= since 0 ⋅ 11 = 0. 6. 11 0 is undefined because there is no number that when multiplied by 0 gives 11. 7. 1 1 5 15 5 4 4 5 45 20 ⋅ = ⋅ = = ⋅ 8. 20 225 4 35 57 7 ⋅ ⋅ = = ⋅ 9. 7 20 is already simplified. 10. 12 43 3 40 410 10 ⋅ = = ⋅ 11. ⋅ ⋅ ⋅ ⋅ = = = ⋅ ⋅ ⋅ 12. 2 3 2 4 24 8 9 4 9 3 93 27 ⋅ ÷ = ⋅ = = ⋅ 13. 8 8 24 8 1 ⋅ ÷ = ÷ = ⋅ = = ⋅ ⋅ 14. 2 3 ⋅ ⋅ ÷ = ⋅ = = ⋅ ⋅ 15. 2 5 2 5 7 + + = = 16. 1 3 1 3 4 4 1 8 8 8 8 24 2 + + = = = = ⋅ 17. 7 2 7 2 5 6 6 6 6 − − = = 18. − − = = = 19. 3 1 3 5 1 2 15 2 17 8 20 8 5 20 2 40 40 40 + = ⋅ + ⋅ = + = 20. 8 1 8 1 5 8 5 3 3 1 15 3 15 3 5 − = − ⋅ = − = = = ⋅ 21. 6 6 ; ⋅ + = = 5 5 ⋅ + = = 6 5 6 5 235 15 15 ⋅ ⋅ ⋅ = ⋅ = = = ⋅ ⋅ 22. 14 8 4 8 4 8 8 8 8 + = + = + = = 23. 1 3 3 35 35 35 4 12 12 12 − − − = Vocabulary. Readiness & Video Check R.2 1. The number 17 31 is called a fraction. The number 31 is called its denominator and 17 is called its numerator. 2. The fraction 8 3 is called an improper fraction, the fraction 3 8 is called a proper fraction, and 3 108 is called a mixed number. 3. In 11 48 , since 11 and 48 have no common factors other than 1, 11 48 is in simplest form. 4. Fractions that represent the same portion of a whole are called equivalent fractions. 5. To multiply two fractions, we write .