Solutions Manual for Larson’s Intermediate Algebra : Algebra within Reach
Feb 07, 2022
https://gioumeh.com/product/algebra-within-reach-solution/
-----------------------------------------------------------
Authors: Larson, Ron
Published: Cengage Learning 2013
Edition: 6th
Pages: 386
Type: pdf
Size: 8MB
Welcome message from author
welcome to solution manual
Transcript
The Behrend College
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Intermediate Algebra Algebra Within Reach
SIXTH EDITION
The Behrend College
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest.
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Printed in the United States of America 1 2 3 4 5 6 7 17 16 15 14 13
© 2014 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher.
For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support,
1-800-354-9706
For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions
Further permissions questions can be emailed to [email protected]
ISBN-13: 978-1-285-41985-5 ISBN-10: 1-285-41985-5 Brooks/Cole 20 Channel Center Street Boston, MA 02210 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: www.cengage.com/global Cengage Learning products are represented in Canada by Nelson Education, Ltd. To learn more about Brooks/Cole, visit www.cengage.com/brookscole Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Chapter 2 Linear Equations and Inequalities........................................................17
Chapter 3 Graphs and Functions...........................................................................54
Chapter 5 Polynomials and Factoring.................................................................145
Chapter 7 Radicals and Complex Numbers .......................................................208
Chapter 8 Quadratic Equations, Functions, and Inequalities.............................243
Chapter 9 Exponential and Logarithmic Functions ...........................................286
Chapter 10 Conics..................................................................................................318
iii
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Section 1.1 The Real Number System ......................................................................2
Section 1.2 Operations with Real Numbers..............................................................3
Section 1.3 Properties of Real Numbers ...................................................................6
Mid-Chapter Quiz..........................................................................................................8
Review Exercises ..........................................................................................................14
Chapter Test ...............................................................................................................15
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
C H A P T E R 1 Fundamentals of Algebra
Section 1.1 The Real Number System
1. { }54 3 86, 6, , 0, , 1, 2, 2, , 6π− − −
(a) Natural numbers: { }1, 2, 6
(b) Integers: { }6, 0, 1, 2, 6−
(c) Rational numbers: { }54 3 86, , 0, , 1, 2, 6− −
(d) Irrational numbers: { }6, 2, π−
3. { }31 9 114.2, 4, , 0, , 11, 5.5, 5.543− −
(a) Natural numbers: { }4
(b) Integers: { }4, 0
(c) Rational numbers: { }31 9 114.2, 4, , 0, , 5.5, 5.543−
(d) Irrational numbers: { }11
5. (a) The point representing the real number 3 lies between 2 and 4.
(b) The point representing the real number 5 2 lies
between 2 and 3.
(c) The point representing the real number 7 2− lies
between 4− and 3.−
(d) The point representing the real number 5.2− lies between 6− and 5,− but closer to 5.−
7. 4 5 1< because 4
5 is to the left of 1 on the real number
line.
9. 5 2− < because 5− is to the left of 2 on the real number line.
11. 5 2− < − because 5− is to the left of 2− on the real number line.
13. 5 1 8 2> because 5
8 is to the right of 1 2 on the real number
line.
15. 102 3 3− > − because 2
3− is to the right of 10 3− on the real
number line.
19. Distance ( )7 12 7 12 19= − − = + =
21. Distance ( )18 32 18 32 50= − − = + =
23. Distance ( )0 8 0 8 8= − − = + =
25. Distance 35 0 35= − =
27. Distance ( ) ( ) ( )6 9 6 9 3= − − − = − + =
29. 10 10=
31. 225 225− =
33. 3 3 4 4− − = −
35. 6 2− > because 6 6− = and 2 2,= and 6 is greater than 2.
37. 47 27> − because 47 47= and 27 27,− = and 47 is greater than 27.
39. Label: The weight on the elevator x=
Inequality: 2500x ≤
Inequality: 200x >
Inequality: 52x ≥
Inequality: 200 700x≤ ≤
47. The number line shows 2.5 2− < because 2.5− is to the left of 2.−
49. The fractions are converted to decimals and plotted on a number line to determine the order.
43210
3
2 7−
−5.2
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
51. { }5, 4, 3, 2, 1, 0, 1, 2, 3− − − − −
53. { }5, 7, 9
55. 1 21,a b= − =
9 2 2− < −
59. 85 85− − = −
61. 3.5 3.5− = −
63. π π− =
65. The opposite of 7− is 7.
The distance of both 7− and 7 from 0 is 7.
67. The opposite of 5 is 5− .
The distance of both 5− and 5 from 0 is 5.
69. The opposite of 3 5− is 3
5.
5 from 0 is 3 5.
71. The opposite of 5 3 is 5
3.−
3− from 0 is 5 3.
73. The opposite of 4.25− is 4.25.
The distance of both 4.25− and 4.25 from 0 is 4.25.
75. 0x <
77. 16u ≥
79. You have more than 30 coins and fewer than 50 coins in a jar.
81. Because 4 4− = and 4 4,= the two possible values of a are 4− and 4.
83. Because 2 3 5 5− − = − = and 8 3 5 5,− = = the two possible values of a are 2− and 8.
85. Sample answers: 4 13, 100,− − −
87. Sample answers: 2, , 3 3π −
89. Sample answers: 3 1 4 2,1 , 0.16
91. Sample answers: 1 2, , 2π− −
93. True. If a number can be written as ratio of two integers, it is rational. If not, the number is irrational.
95. 15 1000.15 = and 15
990.15 0.151515= =…
7. ( ) ( )8 12 8 12 8 12 20− − = − + − = − + = −
9. 13 ( 9) 13 9 22− − = + =
11. 15 ( 18) 15 18 (18 15) 3− − − = − + = + − =
+ + = = =
− − = = =
( ) ( )
3 2 1 53 1 5 2 5 2 2 5
6 5 10 10 6 5
10 1
−5 5
−4.25 4.25
64
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
4 Chapter 1 Fundamentals of Algebra
− − = = = =
⋅
7 4 35 2 4 8
28 35 8 8 28 35
8 63 8
25 285 8 4 2
85 50 8 8
35. 3 8 24 12 2 5 10 5 − = − = −
37. ( )( )5 4 1 8 5 2− − =
39. 18 6 3 6 3 3
− − ⋅ − = =
− −
= = −
45. ( )( ) ( )( ) 4 254 8 4 25 5
5 25 5 8 5 8 2 −
− ÷ = − ⋅ = = −
1 61 6 2 3 5 3 5 5
− ÷ − = − ÷ −
− −− − = ⋅ = =
49. ( )( ) ( )( ) 33 21 1 33 9 33 2 114 4
8 2 8 2 8 9 8 9 12 ÷ = ÷ = ⋅ = =
51.
− ÷ − = − ÷ −
= − ⋅ − = =
53. ( ) ( ) ( ) ( )37 7 7 7− ⋅ − ⋅ − = −
55. ( ) ( ) ( ) ( ) ( )41 1 1 1 1 4 4 4 4 4⋅ ⋅ ⋅ =
57. ( ) 37 7 7 7− ⋅ ⋅ = −
59. ( )( )( )( )( )52 2 2 2 2 2 32= =
61. ( ) ( )( )( )( )42 2 2 2 2 16− = − − − − =
63. ( )( )( )34 4 4 4 64− = − = −
65. ( ) ( )( )( )3 644 4 4 4 5 5 5 5 125= =
67. ( ) ( )( )21 1 1 1 2 2 2 4− = − − =
69. ( ) ( )( )( )( )( ) ( )51 1 1 1 1 1 1 1 2 2 2 2 2 2 32 32− − = − − − − − − = − − =
71. ( ) ( )( )( )30.3 0.3 0.3 0.3 0.027= =
73. ( ) ( )( )( ) ( )35 0.4 5 0.4 0.4 0.4 5 0.064 0.32− = − − − = − = −
75. ( )16 6 10 16 6 10 10 10 0− − = − − = − =
77.
− ⋅ = − ⋅
= − ⋅ = − =
7 15 22
14 8 6
− − = −
= −
=
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
83. ( ) ( ) ( )
17 5 1
17 5 12
25 2 1
25 2 27
125 10 135
7 12 6 24 7 12
30 5
91. Apply the order of operations as follows: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
93. To subtract the real number b from the real number ,a add the opposite of b to a .
95. 85 25 85 25 60− − = − =
97. ( )11.325 34.625 11.325 34.625 45.95− − + = + =
99.
( ) ( )
7 1 7 16 8 6 8 8 4 8 4
33 255 8 4 2
55 66 8 8
11 16 5 11 7
11 11 7
1 7 6
3 3 24 12 9 3
12 12 1
12 3 1 4 4 8
15 1 4 8
15 8 4 1
107. 1 2 1 1 1 4 9 10 3
x+ + + + =
So,
1 2 1 11 4 9 10 3 45 40 18 601
180 180 180 180 45 40 18 601
180 1631 180
x = − + + +
The balance at the end of the month was $2533.56.
111. 14 centimeters, 8 centimetersI w= =
14 8 112 square centimeters
A lw A =
1 2 1 2 10 7 35 square feet
A bh
=
= ⋅ ⋅ =
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
6 Chapter 1 Fundamentals of Algebra
115. True. A nonzero rational number is an integer divided by an integer. The reciprocal of such a number is still an integer divided by an integer, and so it is a rational number.
117. True. Any negative real number raised to an even numbered power will be a positive real number.
119. False. Division is not commutative.
121. If the numbers have like signs, the product or quotient is positive. If the numbers have unlike signs, the product or quotient is negative.
( ) ( )
( ) ( )
2 2 3 32 3 4 9 13 3 2 3 2 2 3 6 6 6 + = + = + =
Section 1.3 Properties of Real Numbers
1. 18 18 0− =
Multiplicative Inverse Property
Distributive Property
9. ( )5 6 5 6 5z z+ = ⋅ + ⋅
11. 4 5 ( 4) 4 5 4
x x
15. ( )( ) ( ) ( )6 2 2 6 2x x+ − = ⋅ − + ⋅ − or 2 12x− −
17. ( ) ( ) ( )( )6 2 5 6 2 6 5y y− − = − + − − or 12 30y− +
19. ( )7 2 7 2 9x x x x+ = + =
, 0 Write original equation. 1 1 Multiplication Property of Equality
1 1 Commutative Property of Multiplication
1 1 Associative Property of Multiplication
1 1 Multipli
ac bc c
a b
25. ( ) ( ) ( )
Write original equation. Associative Property of Addition
0 Additive Inverse Property Additive Identity Property
= + + −
= + + − = +
=
Commutative Property of Addition
Associative Property of Multiplication
Associative Property of Multiplication
33. 110 1 10
Additive Inverse Property
Distributive Property
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
39. ( ) ( )1 1 0x x+ − + =
Additive Inverse Property
( ) ( ) ( ) ( )( )
5 3 Write original equation. 5 5 3 5 Addition Property of Equality 5 5 3 5 Associative Property of Addition
0 2 Additive Inverse Property 2 Additive Identity Property
x x
x x
( ) ( )1 1 2 2
2 5 6 Write original equation. 2 5 5 6 5 Addition Property of Equality
2 5 5 11 Associative Property of Addition 2 0 11 Additive Inverse Property
2 11 Additive Identity Property 2 11 Multiplication Pr
x x
x x
x x
1 Multiplicative Inverse Property Multiplicative Identity Property
x
( ) ( )1 1 4 4
4 4 0 Write original equation. 4 4 4 0 4 Addition Property of Equality
4 ( 4 4) 4 Associative Property of Addition 4 0 4 Additive Inverse Property
4 4 Additive Identity Property 4 4 Multiplicat
x x
x x
x x
1 1 Multiplicative Inverse Property 1 Multiplicative Identity Property
x
− ⋅ − = − ⋅ = −
= −
47. Every real number except zero has an additive inverse. The additive inverse (or opposite) of a number is the same distance from zero as that number. Because there is no distance from zero to zero, zero does not have an additive inverse.
49. No. Subtraction: 8 2 6 6 2 8− = ≠ − = −
Division: 1 321 7 3 7 21÷ = ≠ = ÷
51. ( ) ( )32 4 32 4y y+ + = + +
53. ( ) ( )9 6 9 6M M= ⋅
55. ( )3 5 3 15x x+ = +
57. ( )2 8 2 16x x− + = − −
59. ( ) ( ) ( ) ( )1 1 4 416 1.75 16 2 16 2 16 32 4 28= − = − = − =
61. ( ) ( ) ( ) ( )7 62 7 60 2 7 60 7 2 420 14 434= + = + = + =
63. ( ) ( ) ( ) ( )
9 7 9 0.02
67. ( ) ( ) ( ) ( ) ( ) ( )
4 5 3 2
x x x x
+ + + + = + + +…
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Intermediate Algebra Algebra Within Reach
SIXTH EDITION
The Behrend College
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest.
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Printed in the United States of America 1 2 3 4 5 6 7 17 16 15 14 13
© 2014 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher.
For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support,
1-800-354-9706
For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions
Further permissions questions can be emailed to [email protected]
ISBN-13: 978-1-285-41985-5 ISBN-10: 1-285-41985-5 Brooks/Cole 20 Channel Center Street Boston, MA 02210 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at: www.cengage.com/global Cengage Learning products are represented in Canada by Nelson Education, Ltd. To learn more about Brooks/Cole, visit www.cengage.com/brookscole Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Chapter 2 Linear Equations and Inequalities........................................................17
Chapter 3 Graphs and Functions...........................................................................54
Chapter 5 Polynomials and Factoring.................................................................145
Chapter 7 Radicals and Complex Numbers .......................................................208
Chapter 8 Quadratic Equations, Functions, and Inequalities.............................243
Chapter 9 Exponential and Logarithmic Functions ...........................................286
Chapter 10 Conics..................................................................................................318
iii
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Section 1.1 The Real Number System ......................................................................2
Section 1.2 Operations with Real Numbers..............................................................3
Section 1.3 Properties of Real Numbers ...................................................................6
Mid-Chapter Quiz..........................................................................................................8
Review Exercises ..........................................................................................................14
Chapter Test ...............................................................................................................15
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
C H A P T E R 1 Fundamentals of Algebra
Section 1.1 The Real Number System
1. { }54 3 86, 6, , 0, , 1, 2, 2, , 6π− − −
(a) Natural numbers: { }1, 2, 6
(b) Integers: { }6, 0, 1, 2, 6−
(c) Rational numbers: { }54 3 86, , 0, , 1, 2, 6− −
(d) Irrational numbers: { }6, 2, π−
3. { }31 9 114.2, 4, , 0, , 11, 5.5, 5.543− −
(a) Natural numbers: { }4
(b) Integers: { }4, 0
(c) Rational numbers: { }31 9 114.2, 4, , 0, , 5.5, 5.543−
(d) Irrational numbers: { }11
5. (a) The point representing the real number 3 lies between 2 and 4.
(b) The point representing the real number 5 2 lies
between 2 and 3.
(c) The point representing the real number 7 2− lies
between 4− and 3.−
(d) The point representing the real number 5.2− lies between 6− and 5,− but closer to 5.−
7. 4 5 1< because 4
5 is to the left of 1 on the real number
line.
9. 5 2− < because 5− is to the left of 2 on the real number line.
11. 5 2− < − because 5− is to the left of 2− on the real number line.
13. 5 1 8 2> because 5
8 is to the right of 1 2 on the real number
line.
15. 102 3 3− > − because 2
3− is to the right of 10 3− on the real
number line.
19. Distance ( )7 12 7 12 19= − − = + =
21. Distance ( )18 32 18 32 50= − − = + =
23. Distance ( )0 8 0 8 8= − − = + =
25. Distance 35 0 35= − =
27. Distance ( ) ( ) ( )6 9 6 9 3= − − − = − + =
29. 10 10=
31. 225 225− =
33. 3 3 4 4− − = −
35. 6 2− > because 6 6− = and 2 2,= and 6 is greater than 2.
37. 47 27> − because 47 47= and 27 27,− = and 47 is greater than 27.
39. Label: The weight on the elevator x=
Inequality: 2500x ≤
Inequality: 200x >
Inequality: 52x ≥
Inequality: 200 700x≤ ≤
47. The number line shows 2.5 2− < because 2.5− is to the left of 2.−
49. The fractions are converted to decimals and plotted on a number line to determine the order.
43210
3
2 7−
−5.2
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
51. { }5, 4, 3, 2, 1, 0, 1, 2, 3− − − − −
53. { }5, 7, 9
55. 1 21,a b= − =
9 2 2− < −
59. 85 85− − = −
61. 3.5 3.5− = −
63. π π− =
65. The opposite of 7− is 7.
The distance of both 7− and 7 from 0 is 7.
67. The opposite of 5 is 5− .
The distance of both 5− and 5 from 0 is 5.
69. The opposite of 3 5− is 3
5.
5 from 0 is 3 5.
71. The opposite of 5 3 is 5
3.−
3− from 0 is 5 3.
73. The opposite of 4.25− is 4.25.
The distance of both 4.25− and 4.25 from 0 is 4.25.
75. 0x <
77. 16u ≥
79. You have more than 30 coins and fewer than 50 coins in a jar.
81. Because 4 4− = and 4 4,= the two possible values of a are 4− and 4.
83. Because 2 3 5 5− − = − = and 8 3 5 5,− = = the two possible values of a are 2− and 8.
85. Sample answers: 4 13, 100,− − −
87. Sample answers: 2, , 3 3π −
89. Sample answers: 3 1 4 2,1 , 0.16
91. Sample answers: 1 2, , 2π− −
93. True. If a number can be written as ratio of two integers, it is rational. If not, the number is irrational.
95. 15 1000.15 = and 15
990.15 0.151515= =…
7. ( ) ( )8 12 8 12 8 12 20− − = − + − = − + = −
9. 13 ( 9) 13 9 22− − = + =
11. 15 ( 18) 15 18 (18 15) 3− − − = − + = + − =
+ + = = =
− − = = =
( ) ( )
3 2 1 53 1 5 2 5 2 2 5
6 5 10 10 6 5
10 1
−5 5
−4.25 4.25
64
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
4 Chapter 1 Fundamentals of Algebra
− − = = = =
⋅
7 4 35 2 4 8
28 35 8 8 28 35
8 63 8
25 285 8 4 2
85 50 8 8
35. 3 8 24 12 2 5 10 5 − = − = −
37. ( )( )5 4 1 8 5 2− − =
39. 18 6 3 6 3 3
− − ⋅ − = =
− −
= = −
45. ( )( ) ( )( ) 4 254 8 4 25 5
5 25 5 8 5 8 2 −
− ÷ = − ⋅ = = −
1 61 6 2 3 5 3 5 5
− ÷ − = − ÷ −
− −− − = ⋅ = =
49. ( )( ) ( )( ) 33 21 1 33 9 33 2 114 4
8 2 8 2 8 9 8 9 12 ÷ = ÷ = ⋅ = =
51.
− ÷ − = − ÷ −
= − ⋅ − = =
53. ( ) ( ) ( ) ( )37 7 7 7− ⋅ − ⋅ − = −
55. ( ) ( ) ( ) ( ) ( )41 1 1 1 1 4 4 4 4 4⋅ ⋅ ⋅ =
57. ( ) 37 7 7 7− ⋅ ⋅ = −
59. ( )( )( )( )( )52 2 2 2 2 2 32= =
61. ( ) ( )( )( )( )42 2 2 2 2 16− = − − − − =
63. ( )( )( )34 4 4 4 64− = − = −
65. ( ) ( )( )( )3 644 4 4 4 5 5 5 5 125= =
67. ( ) ( )( )21 1 1 1 2 2 2 4− = − − =
69. ( ) ( )( )( )( )( ) ( )51 1 1 1 1 1 1 1 2 2 2 2 2 2 32 32− − = − − − − − − = − − =
71. ( ) ( )( )( )30.3 0.3 0.3 0.3 0.027= =
73. ( ) ( )( )( ) ( )35 0.4 5 0.4 0.4 0.4 5 0.064 0.32− = − − − = − = −
75. ( )16 6 10 16 6 10 10 10 0− − = − − = − =
77.
− ⋅ = − ⋅
= − ⋅ = − =
7 15 22
14 8 6
− − = −
= −
=
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
83. ( ) ( ) ( )
17 5 1
17 5 12
25 2 1
25 2 27
125 10 135
7 12 6 24 7 12
30 5
91. Apply the order of operations as follows: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
93. To subtract the real number b from the real number ,a add the opposite of b to a .
95. 85 25 85 25 60− − = − =
97. ( )11.325 34.625 11.325 34.625 45.95− − + = + =
99.
( ) ( )
7 1 7 16 8 6 8 8 4 8 4
33 255 8 4 2
55 66 8 8
11 16 5 11 7
11 11 7
1 7 6
3 3 24 12 9 3
12 12 1
12 3 1 4 4 8
15 1 4 8
15 8 4 1
107. 1 2 1 1 1 4 9 10 3
x+ + + + =
So,
1 2 1 11 4 9 10 3 45 40 18 601
180 180 180 180 45 40 18 601
180 1631 180
x = − + + +
The balance at the end of the month was $2533.56.
111. 14 centimeters, 8 centimetersI w= =
14 8 112 square centimeters
A lw A =
1 2 1 2 10 7 35 square feet
A bh
=
= ⋅ ⋅ =
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
6 Chapter 1 Fundamentals of Algebra
115. True. A nonzero rational number is an integer divided by an integer. The reciprocal of such a number is still an integer divided by an integer, and so it is a rational number.
117. True. Any negative real number raised to an even numbered power will be a positive real number.
119. False. Division is not commutative.
121. If the numbers have like signs, the product or quotient is positive. If the numbers have unlike signs, the product or quotient is negative.
( ) ( )
( ) ( )
2 2 3 32 3 4 9 13 3 2 3 2 2 3 6 6 6 + = + = + =
Section 1.3 Properties of Real Numbers
1. 18 18 0− =
Multiplicative Inverse Property
Distributive Property
9. ( )5 6 5 6 5z z+ = ⋅ + ⋅
11. 4 5 ( 4) 4 5 4
x x
15. ( )( ) ( ) ( )6 2 2 6 2x x+ − = ⋅ − + ⋅ − or 2 12x− −
17. ( ) ( ) ( )( )6 2 5 6 2 6 5y y− − = − + − − or 12 30y− +
19. ( )7 2 7 2 9x x x x+ = + =
, 0 Write original equation. 1 1 Multiplication Property of Equality
1 1 Commutative Property of Multiplication
1 1 Associative Property of Multiplication
1 1 Multipli
ac bc c
a b
25. ( ) ( ) ( )
Write original equation. Associative Property of Addition
0 Additive Inverse Property Additive Identity Property
= + + −
= + + − = +
=
Commutative Property of Addition
Associative Property of Multiplication
Associative Property of Multiplication
33. 110 1 10
Additive Inverse Property
Distributive Property
Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
39. ( ) ( )1 1 0x x+ − + =
Additive Inverse Property
( ) ( ) ( ) ( )( )
5 3 Write original equation. 5 5 3 5 Addition Property of Equality 5 5 3 5 Associative Property of Addition
0 2 Additive Inverse Property 2 Additive Identity Property
x x
x x
( ) ( )1 1 2 2
2 5 6 Write original equation. 2 5 5 6 5 Addition Property of Equality
2 5 5 11 Associative Property of Addition 2 0 11 Additive Inverse Property
2 11 Additive Identity Property 2 11 Multiplication Pr
x x
x x
x x
1 Multiplicative Inverse Property Multiplicative Identity Property
x
( ) ( )1 1 4 4
4 4 0 Write original equation. 4 4 4 0 4 Addition Property of Equality
4 ( 4 4) 4 Associative Property of Addition 4 0 4 Additive Inverse Property
4 4 Additive Identity Property 4 4 Multiplicat
x x
x x
x x
1 1 Multiplicative Inverse Property 1 Multiplicative Identity Property
x
− ⋅ − = − ⋅ = −
= −
47. Every real number except zero has an additive inverse. The additive inverse (or opposite) of a number is the same distance from zero as that number. Because there is no distance from zero to zero, zero does not have an additive inverse.
49. No. Subtraction: 8 2 6 6 2 8− = ≠ − = −
Division: 1 321 7 3 7 21÷ = ≠ = ÷
51. ( ) ( )32 4 32 4y y+ + = + +
53. ( ) ( )9 6 9 6M M= ⋅
55. ( )3 5 3 15x x+ = +
57. ( )2 8 2 16x x− + = − −
59. ( ) ( ) ( ) ( )1 1 4 416 1.75 16 2 16 2 16 32 4 28= − = − = − =
61. ( ) ( ) ( ) ( )7 62 7 60 2 7 60 7 2 420 14 434= + = + = + =
63. ( ) ( ) ( ) ( )
9 7 9 0.02
67. ( ) ( ) ( ) ( ) ( ) ( )
4 5 3 2
x x x x
+ + + + = + + +…
Related Documents
