,SOLUTION MANUAL College Algebra Enhanced
with Graphing Utilities, 9th edition Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, INSTRUCTOR’S SOLUTIONS
MANUAL
GEX INC.
COLLEGE ALGEBRA
ENHANCED WITH GRAPHING
UTILITIES
NINTH EDITION
Michael Sullivan
Chicago State University
Michael Sullivan, III
Joliet Junior College
and
Florida SouthWestern State College
,Copyright © 2026, 2021, 2017 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured 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 www.pearsoned.com/permissions/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are
for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
PPID: A103000398841
, Table of Contents
Chapter R Review
R.1 Real Numbers .......................................................................................................................... 1
R.2 Algebra Essentials ................................................................................................................... 5
R.3 Geometry Essentials .............................................................................................................. 11
R.4 Polynomials ........................................................................................................................... 16
R.5 Factoring Polynomials ........................................................................................................... 23
R.6 Synthetic Division ................................................................................................................. 28
R.7 Rational Expressions ............................................................................................................. 30
R.8 nth Roots; Rational Exponents .............................................................................................. 40
Chapter 1 Graphs, Equations, and Inequalities
1.1 Graphing Utilities; Introduction to Graphing Equations ....................................................... 50
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations....................... 57
1.3 Quadratic Equations .............................................................................................................. 71
1.4 Complex Numbers; Quadratic Equations in the Complex Number System .......................... 89
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ............................................................................................................. 95
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate
Job Applications .................................................................................................................. 115
1.7 Solving Inequalities ............................................................................................................. 123
Chapter Review ............................................................................................................................ 134
Chapter Test ................................................................................................................................. 145
Chapter Project ............................................................................................................................. 149
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................. 150
2.2 Intercepts; Symmetry; Graphing Key Equations ................................................................. 162
2.3 Lines .................................................................................................................................... 178
2.4 Circles .................................................................................................................................. 195
2.5 Variation .............................................................................................................................. 208
Chapter Review ............................................................................................................................ 214
Chapter Test ................................................................................................................................. 220
Cumulative Review ...................................................................................................................... 221
Chapter Project ............................................................................................................................. 224
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................. 225
3.2 The Graph of a Function ...................................................................................................... 243
3.3 Properties of Functions ........................................................................................................ 252
3.4 Library of Functions; Piecewise-defined Functions ............................................................ 269
3.5 Graphing Techniques: Transformations .............................................................................. 282
3.6 Mathematical Models: Building Functions.......................................................................... 300
Chapter Review ............................................................................................................................ 307
Chapter Test ................................................................................................................................. 314
Cumulative Review ...................................................................................................................... 318
Chapter Projects ........................................................................................................................... 321
Copyright © 2026 Pearson Education, Inc.
,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models.............................................................. 322
4.2 Building Linear Models from Data ...................................................................................... 333
4.3 Quadratic Functions and Their Properties ........................................................................... 339
4.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 363
4.5 Inequalities Involving Quadratic Functions ......................................................................... 371
Chapter Review ............................................................................................................................ 390
Chapter Test ................................................................................................................................. 398
Cumulative Review ...................................................................................................................... 400
Chapter Project ............................................................................................................................. 403
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions .......................................................................................................... 404
5.2 The Graph of a Polynomial Function; Models .................................................................... 414
5.3 The Real Zeros of a Polynomial Function ........................................................................... 435
5.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 472
5.5 Properties of Rational Functions ......................................................................................... 481
5.6 The Graph of a Rational Function ....................................................................................... 491
5.7 Polynomial and Rational Inequalities .................................................................................. 546
Chapter Review ............................................................................................................................ 567
Chapter Test ................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 587
Chapter Project ............................................................................................................................. 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ........................................................................................................... 592
6.2 One-to-One Functions; Inverse Functions ........................................................................... 610
6.3 Exponential Functions ......................................................................................................... 633
6.4 Logarithmic Functions ......................................................................................................... 654
6.5 Properties of Logarithms ..................................................................................................... 676
6.6 Logarithmic and Exponential Equations.............................................................................. 685
6.7 Financial Models ................................................................................................................. 708
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 716
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 728
Chapter Review ............................................................................................................................ 734
Chapter Test ................................................................................................................................. 746
Cumulative Review ...................................................................................................................... 750
Chapter Project ............................................................................................................................. 753
Copyright © 2026 Pearson Education, Inc.
,Chapter 7 Conics
7.2 The Parabola ........................................................................................................................ 754
7.3 The Ellipse ........................................................................................................................... 769
7.4 The Hyperbola ..................................................................................................................... 787
Chapter Review ............................................................................................................................ 807
Chapter Test ................................................................................................................................. 812
Cumulative Review ...................................................................................................................... 814
Chapter Project ............................................................................................................................. 815
Chapter 8 Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination ............................................... 816
8.2 Systems of Linear Equations: Matrices ............................................................................... 838
8.3 Systems of Linear Equations: Determinants ........................................................................ 863
8.4 Matrix Algebra .................................................................................................................... 877
8.5 Partial Fraction Decomposition ........................................................................................... 894
8.6 Systems of Nonlinear Equations .......................................................................................... 912
8.7 Systems of Inequalities ........................................................................................................ 941
8.8 Linear Programming ............................................................................................................ 956
Chapter Review ............................................................................................................................ 969
Chapter Test ................................................................................................................................. 984
Cumulative Review ...................................................................................................................... 992
Chapter Project............................................................................................................................. 996
Chapter 9 Sequences; Induction; the Binomial Theorem
9.1 Sequences ............................................................................................................................ 997
9.2 Arithmetic Sequences ........................................................................................................ 1010
9.3 Geometric Sequences; Geometric Series ........................................................................... 1019
9.4 The Limit of a Sequence; Infinite Series ........................................................................... 1030
9.5 Mathematical Induction ..................................................................................................... 1035
9.6 The Binomial Theorem ...................................................................................................... 1043
Chapter Review .......................................................................................................................... 1050
Chapter Test ............................................................................................................................... 1054
Cumulative Review .................................................................................................................... 1057
Chapter Project ........................................................................................................................... 1059
Chapter 10 Counting and Probability
10.1 Counting ............................................................................................................................ 1060
10.2 Permutations and Combinations ........................................................................................ 1063
10.3 Probability ......................................................................................................................... 1068
Chapter Review .......................................................................................................................... 1075
Chapter Test ............................................................................................................................... 1077
Cumulative Review .................................................................................................................... 1078
Chapter Project ........................................................................................................................... 1081
Copyright © 2026 Pearson Education, Inc.
,
, Chapter R
Review
Section R.1 16. ( A ∩ B) ∪ C
= ({1, 3, 4,5, 9} ∩ {2, 4, 6, 7,8} ) ∪ {1,3, 4, 6}
1. rational
= {4} ∪ {1, 3, 4, 6}
2. 4 + 5 ⋅ 6 − 3 = 4 + 30 − 3 = 31
= {1,3, 4, 6}
3. Distributive
17. A = {0, 2, 6, 7, 8}
4. c
5. a 18. C = {0, 2, 5, 7, 8, 9}
6. b 19. A ∩ B = {1, 3, 4, 5, 9} ∩ {2, 4, 6, 7, 8}
7. True = {4} = {0, 1, 2, 3, 5, 6, 7, 8, 9}
8. False; The Zero-Product Property states that if a
product equals 0, then at least one of the factors 20. B ∪ C = {2, 4, 6, 7, 8} ∪ {1, 3, 4, 6}
must equal 0.
= {1, 2, 3, 4, 6, 7, 8} = {0, 5, 9}
9. False; 6 is the Greatest Common Factor of 12
and 18. The Least Common Multiple is the 21. A ∪ B = {0, 2, 6, 7, 8} ∪ {0, 1, 3, 5, 9}
smallest value that both numbers will divide
= {0, 1, 2, 3, 5, 6, 7, 8, 9}
evenly. The LCM for 12 and 18 is 36.
10. True 22. B ∩ C = {0, 1, 3, 5, 9} ∩ {0, 2, 5, 7, 8, 9}
= {0, 5, 9}
11. A ∪ B = {1, 3, 4,5, 9} ∪ {2, 4, 6, 7,8}
= {1, 2,3, 4, 5, 6, 7,8, 9}
23. a. {2,5}
12. A ∪ C = {1, 3, 4,5, 9} ∪ {1, 3, 4, 6} b. {−6, 2,5}
= {1, 3, 4, 5, 6, 9}
13. A ∩ B = {1, 3, 4,5, 9} ∩ {2, 4, 6, 7,8} = {4}
c. { 1
−6, , −1.333... = −1.3, 2,5
2 }
d. {π }
14. A ∩ C = {1, 3, 4,5, 9} ∩ {1, 3, 4, 6} = {1, 3, 4}
15. ( A ∪ B) ∩ C
e. { 1
−6, , −1.333... = −1.3, π , 2,5
2 }
= ({1, 3, 4,5, 9} ∪ {2, 4, 6, 7,8} ) ∩ {1,3, 4, 6} 24. a. {1}
= {1, 2,3, 4,5, 6, 7,8,9} ∩ {1,3, 4, 6}
b. {0,1}
= {1, 3, 4, 6}
c. { 5
− , 2.060606... = 2.06,1.25, 0,1
3 }
d. { 5}
1
Copyright © 2026 Pearson Education, Inc.
, Chapter R: Review
e. { 5
− , 2.060606... = 2.06,1.25, 0,1, 5
3 } 34. a.
35. a.
0.054
9.999
b.
b.
0.053
9.998
25. a. {1} 36. a. 1.001 b. 1.000
b. {0,1} 37. a. 0.429 b. 0.428
c. { 1 1 1
0,1, , ,
2 3 4 } 38. a. 0.556 b. 0.555
d. None 39. a. 34.733 b. 34.733
e. { 1 1 1
0,1, , ,
2 3 4 } 40. a. 16.200
41. 3 + 2 = 5
b. 16.200
26. a. None
42. 5 ⋅ 2 = 10
b. {−1}
43. x + 2 = 3 ⋅ 4
c. {−1.3, −1.2, −1.1, −1}
44. 3 + y = 2 + 2
d. None
e. {−1.3, −1.2, −1.1, −1} 45. 3 y = 1 + 2
46. 2 x = 4 ⋅ 6
27. a. None
b. None 47. x − 2 = 6
c. None
48. 2 − y = 6
d. { 2, π , 2 + 1, π +
1
2 } 49.
x
=6
2
e. { 2, π , 2 + 1, π +
1
2 } 50.
2
=6
x
28. a. None
b. None 51. 9 − 4 + 2 = 5 + 2 = 7
c. { 1
2 }
+ 10.3
52. 6 − 4 + 3 = 2 + 3 = 5
53. −6 + 4 ⋅ 3 = −6 + 12 = 6
d. {− 2, π + 2 } 54. 8 − 4 ⋅ 2 = 8 − 8 = 0
e. { 1
− 2, π + 2, + 10.3
2 } 55. 18 − 5 ⋅ 2 = 18 − 10 = 8
56. 100 − 10 ⋅ 2 = 100 − 20 = 80
29. a. 18.953 b. 18.952
1 12 + 1 13
30. a. 25.861 b. 25.861 57. 4 + = =
3 3 3
31. a. 28.653 b. 28.653
1 4 −1 3
58. 2 − = =
32. a. 99.052 b. 99.052 2 2 2
33. a. 0.063 b. 0.062
2
Copyright © 2026 Pearson Education, Inc.
with Graphing Utilities, 9th edition Sullivan
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, INSTRUCTOR’S SOLUTIONS
MANUAL
GEX INC.
COLLEGE ALGEBRA
ENHANCED WITH GRAPHING
UTILITIES
NINTH EDITION
Michael Sullivan
Chicago State University
Michael Sullivan, III
Joliet Junior College
and
Florida SouthWestern State College
,Copyright © 2026, 2021, 2017 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Manufactured 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 www.pearsoned.com/permissions/.
PEARSON and MYLAB are exclusive trademarks owned by Pearson Education, Inc. or its affiliates in the U.S.
and/or other countries.
Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the
property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are
for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship,
endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship
between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors.
PPID: A103000398841
, Table of Contents
Chapter R Review
R.1 Real Numbers .......................................................................................................................... 1
R.2 Algebra Essentials ................................................................................................................... 5
R.3 Geometry Essentials .............................................................................................................. 11
R.4 Polynomials ........................................................................................................................... 16
R.5 Factoring Polynomials ........................................................................................................... 23
R.6 Synthetic Division ................................................................................................................. 28
R.7 Rational Expressions ............................................................................................................. 30
R.8 nth Roots; Rational Exponents .............................................................................................. 40
Chapter 1 Graphs, Equations, and Inequalities
1.1 Graphing Utilities; Introduction to Graphing Equations ....................................................... 50
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations....................... 57
1.3 Quadratic Equations .............................................................................................................. 71
1.4 Complex Numbers; Quadratic Equations in the Complex Number System .......................... 89
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations;
Factorable Equations ............................................................................................................. 95
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate
Job Applications .................................................................................................................. 115
1.7 Solving Inequalities ............................................................................................................. 123
Chapter Review ............................................................................................................................ 134
Chapter Test ................................................................................................................................. 145
Chapter Project ............................................................................................................................. 149
Chapter 2 Graphs
2.1 The Distance and Midpoint Formulas ................................................................................. 150
2.2 Intercepts; Symmetry; Graphing Key Equations ................................................................. 162
2.3 Lines .................................................................................................................................... 178
2.4 Circles .................................................................................................................................. 195
2.5 Variation .............................................................................................................................. 208
Chapter Review ............................................................................................................................ 214
Chapter Test ................................................................................................................................. 220
Cumulative Review ...................................................................................................................... 221
Chapter Project ............................................................................................................................. 224
Chapter 3 Functions and Their Graphs
3.1 Functions ............................................................................................................................. 225
3.2 The Graph of a Function ...................................................................................................... 243
3.3 Properties of Functions ........................................................................................................ 252
3.4 Library of Functions; Piecewise-defined Functions ............................................................ 269
3.5 Graphing Techniques: Transformations .............................................................................. 282
3.6 Mathematical Models: Building Functions.......................................................................... 300
Chapter Review ............................................................................................................................ 307
Chapter Test ................................................................................................................................. 314
Cumulative Review ...................................................................................................................... 318
Chapter Projects ........................................................................................................................... 321
Copyright © 2026 Pearson Education, Inc.
,Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models.............................................................. 322
4.2 Building Linear Models from Data ...................................................................................... 333
4.3 Quadratic Functions and Their Properties ........................................................................... 339
4.4 Build Quadratic Models from Verbal Descriptions and from Data ..................................... 363
4.5 Inequalities Involving Quadratic Functions ......................................................................... 371
Chapter Review ............................................................................................................................ 390
Chapter Test ................................................................................................................................. 398
Cumulative Review ...................................................................................................................... 400
Chapter Project ............................................................................................................................. 403
Chapter 5 Polynomial and Rational Functions
5.1 Polynomial Functions .......................................................................................................... 404
5.2 The Graph of a Polynomial Function; Models .................................................................... 414
5.3 The Real Zeros of a Polynomial Function ........................................................................... 435
5.4 Complex Zeros; Fundamental Theorem of Algebra ............................................................ 472
5.5 Properties of Rational Functions ......................................................................................... 481
5.6 The Graph of a Rational Function ....................................................................................... 491
5.7 Polynomial and Rational Inequalities .................................................................................. 546
Chapter Review ............................................................................................................................ 567
Chapter Test ................................................................................................................................. 582
Cumulative Review ...................................................................................................................... 587
Chapter Project ............................................................................................................................. 591
Chapter 6 Exponential and Logarithmic Functions
6.1 Composite Functions ........................................................................................................... 592
6.2 One-to-One Functions; Inverse Functions ........................................................................... 610
6.3 Exponential Functions ......................................................................................................... 633
6.4 Logarithmic Functions ......................................................................................................... 654
6.5 Properties of Logarithms ..................................................................................................... 676
6.6 Logarithmic and Exponential Equations.............................................................................. 685
6.7 Financial Models ................................................................................................................. 708
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models ............................................................................................................... 716
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................. 728
Chapter Review ............................................................................................................................ 734
Chapter Test ................................................................................................................................. 746
Cumulative Review ...................................................................................................................... 750
Chapter Project ............................................................................................................................. 753
Copyright © 2026 Pearson Education, Inc.
,Chapter 7 Conics
7.2 The Parabola ........................................................................................................................ 754
7.3 The Ellipse ........................................................................................................................... 769
7.4 The Hyperbola ..................................................................................................................... 787
Chapter Review ............................................................................................................................ 807
Chapter Test ................................................................................................................................. 812
Cumulative Review ...................................................................................................................... 814
Chapter Project ............................................................................................................................. 815
Chapter 8 Systems of Equations and Inequalities
8.1 Systems of Linear Equations: Substitution and Elimination ............................................... 816
8.2 Systems of Linear Equations: Matrices ............................................................................... 838
8.3 Systems of Linear Equations: Determinants ........................................................................ 863
8.4 Matrix Algebra .................................................................................................................... 877
8.5 Partial Fraction Decomposition ........................................................................................... 894
8.6 Systems of Nonlinear Equations .......................................................................................... 912
8.7 Systems of Inequalities ........................................................................................................ 941
8.8 Linear Programming ............................................................................................................ 956
Chapter Review ............................................................................................................................ 969
Chapter Test ................................................................................................................................. 984
Cumulative Review ...................................................................................................................... 992
Chapter Project............................................................................................................................. 996
Chapter 9 Sequences; Induction; the Binomial Theorem
9.1 Sequences ............................................................................................................................ 997
9.2 Arithmetic Sequences ........................................................................................................ 1010
9.3 Geometric Sequences; Geometric Series ........................................................................... 1019
9.4 The Limit of a Sequence; Infinite Series ........................................................................... 1030
9.5 Mathematical Induction ..................................................................................................... 1035
9.6 The Binomial Theorem ...................................................................................................... 1043
Chapter Review .......................................................................................................................... 1050
Chapter Test ............................................................................................................................... 1054
Cumulative Review .................................................................................................................... 1057
Chapter Project ........................................................................................................................... 1059
Chapter 10 Counting and Probability
10.1 Counting ............................................................................................................................ 1060
10.2 Permutations and Combinations ........................................................................................ 1063
10.3 Probability ......................................................................................................................... 1068
Chapter Review .......................................................................................................................... 1075
Chapter Test ............................................................................................................................... 1077
Cumulative Review .................................................................................................................... 1078
Chapter Project ........................................................................................................................... 1081
Copyright © 2026 Pearson Education, Inc.
,
, Chapter R
Review
Section R.1 16. ( A ∩ B) ∪ C
= ({1, 3, 4,5, 9} ∩ {2, 4, 6, 7,8} ) ∪ {1,3, 4, 6}
1. rational
= {4} ∪ {1, 3, 4, 6}
2. 4 + 5 ⋅ 6 − 3 = 4 + 30 − 3 = 31
= {1,3, 4, 6}
3. Distributive
17. A = {0, 2, 6, 7, 8}
4. c
5. a 18. C = {0, 2, 5, 7, 8, 9}
6. b 19. A ∩ B = {1, 3, 4, 5, 9} ∩ {2, 4, 6, 7, 8}
7. True = {4} = {0, 1, 2, 3, 5, 6, 7, 8, 9}
8. False; The Zero-Product Property states that if a
product equals 0, then at least one of the factors 20. B ∪ C = {2, 4, 6, 7, 8} ∪ {1, 3, 4, 6}
must equal 0.
= {1, 2, 3, 4, 6, 7, 8} = {0, 5, 9}
9. False; 6 is the Greatest Common Factor of 12
and 18. The Least Common Multiple is the 21. A ∪ B = {0, 2, 6, 7, 8} ∪ {0, 1, 3, 5, 9}
smallest value that both numbers will divide
= {0, 1, 2, 3, 5, 6, 7, 8, 9}
evenly. The LCM for 12 and 18 is 36.
10. True 22. B ∩ C = {0, 1, 3, 5, 9} ∩ {0, 2, 5, 7, 8, 9}
= {0, 5, 9}
11. A ∪ B = {1, 3, 4,5, 9} ∪ {2, 4, 6, 7,8}
= {1, 2,3, 4, 5, 6, 7,8, 9}
23. a. {2,5}
12. A ∪ C = {1, 3, 4,5, 9} ∪ {1, 3, 4, 6} b. {−6, 2,5}
= {1, 3, 4, 5, 6, 9}
13. A ∩ B = {1, 3, 4,5, 9} ∩ {2, 4, 6, 7,8} = {4}
c. { 1
−6, , −1.333... = −1.3, 2,5
2 }
d. {π }
14. A ∩ C = {1, 3, 4,5, 9} ∩ {1, 3, 4, 6} = {1, 3, 4}
15. ( A ∪ B) ∩ C
e. { 1
−6, , −1.333... = −1.3, π , 2,5
2 }
= ({1, 3, 4,5, 9} ∪ {2, 4, 6, 7,8} ) ∩ {1,3, 4, 6} 24. a. {1}
= {1, 2,3, 4,5, 6, 7,8,9} ∩ {1,3, 4, 6}
b. {0,1}
= {1, 3, 4, 6}
c. { 5
− , 2.060606... = 2.06,1.25, 0,1
3 }
d. { 5}
1
Copyright © 2026 Pearson Education, Inc.
, Chapter R: Review
e. { 5
− , 2.060606... = 2.06,1.25, 0,1, 5
3 } 34. a.
35. a.
0.054
9.999
b.
b.
0.053
9.998
25. a. {1} 36. a. 1.001 b. 1.000
b. {0,1} 37. a. 0.429 b. 0.428
c. { 1 1 1
0,1, , ,
2 3 4 } 38. a. 0.556 b. 0.555
d. None 39. a. 34.733 b. 34.733
e. { 1 1 1
0,1, , ,
2 3 4 } 40. a. 16.200
41. 3 + 2 = 5
b. 16.200
26. a. None
42. 5 ⋅ 2 = 10
b. {−1}
43. x + 2 = 3 ⋅ 4
c. {−1.3, −1.2, −1.1, −1}
44. 3 + y = 2 + 2
d. None
e. {−1.3, −1.2, −1.1, −1} 45. 3 y = 1 + 2
46. 2 x = 4 ⋅ 6
27. a. None
b. None 47. x − 2 = 6
c. None
48. 2 − y = 6
d. { 2, π , 2 + 1, π +
1
2 } 49.
x
=6
2
e. { 2, π , 2 + 1, π +
1
2 } 50.
2
=6
x
28. a. None
b. None 51. 9 − 4 + 2 = 5 + 2 = 7
c. { 1
2 }
+ 10.3
52. 6 − 4 + 3 = 2 + 3 = 5
53. −6 + 4 ⋅ 3 = −6 + 12 = 6
d. {− 2, π + 2 } 54. 8 − 4 ⋅ 2 = 8 − 8 = 0
e. { 1
− 2, π + 2, + 10.3
2 } 55. 18 − 5 ⋅ 2 = 18 − 10 = 8
56. 100 − 10 ⋅ 2 = 100 − 20 = 80
29. a. 18.953 b. 18.952
1 12 + 1 13
30. a. 25.861 b. 25.861 57. 4 + = =
3 3 3
31. a. 28.653 b. 28.653
1 4 −1 3
58. 2 − = =
32. a. 99.052 b. 99.052 2 2 2
33. a. 0.063 b. 0.062
2
Copyright © 2026 Pearson Education, Inc.
