Beginning & Intermediate Algebra – 8th Edition
ST
SOLUTIONS
UV
MANUAL
IA
_A
Elayn Martin-Gay
PP
Comprehensive Solutions Manual for Instructors and
RO
Students
© Elayn Martin-Gay
VE
All rights reserved. Reproduction or distribution without permission is prohibited.
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©STUDYSTREAM
, Contents
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UV
Chapter 1 1
Chapter 2 34
IA
Chapter 3 104
Chapter 4 160
_A
Chapter 5 212
Chapter 6 253
PP
Chapter 7 295
Chapter 8 368
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Chapter 9 410
Appendix A 467
Appendix B 469
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Appendix C 471
Appendix D 473
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Practice Final Exam 475
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, Chapter 1
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Section 1.2 Practice Exercises 12 12
c. 3= since simplifies to 3.
4 4
1. a. 5 < 8 since 5 is to the left of 8 on the number
line. 7. a. |−8| = 8 since −8 is 8 units from 0 on a
number line.
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b. 6 > 4 since 6 is to the right of 4 on the
number line. b. |9| = 9 since 9 is 9 units from 0 on a number
line.
c. 16 < 82 since 16 is to the left of 82 on the
number line.
c. |−2.5| = 2.5 since −2.5 is 2.5 units from 0 on
a number line.
2. a. 9 ≥ 3 is true, since 9 > 3 is true.
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b. 3 ≥ 8 is false, since neither 3 > 8 nor 3 = 8 is 5 5 5 5
d. = since is unit from 0 on a
true. 11 11 11 11
number line.
c. 25 ≤ 25 is true, since 25 = 25 is true.
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1 1 1 1
d. 4 ≤ 14 is true, since 4 < 14 is true. e. − = since − is unit from 0 on a
2 2 2 2
3. a. 3<8 number line.
b. 15 ≥ 9 8. a. |8| = |−8| since 8 = 8.
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c. 6≠7 b. |−3| > 0 since 3 > 0.
4. The integer −10 represents 10 meters below sea c. |−7| < |−11| since 7 < 11.
level.
d. |3| > |2| since 3 > 2.
5. a. The natural number is 25.
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e. |0| < |−4| since 0 < 4.
b. The whole number is 25.
Vocabulary, Readiness & Video Check 1.2
c. The integers are 25, −15, −99.
1. The whole numbers are {0, 1, 2, 3, 4, ...}.
7 3 2. The natural numbers are {1, 2, 3, 4, 5, ...}.
d. The rational numbers are 25, , −15, − ,
3 4
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−3.7, 8.8, −99. 3. The symbols ≠, ≤, and > are called inequality
symbols.
e. The irrational number is 5.
4. The integers are {..., −3, −2, −1, 0, 1, 2, 3, ...}.
7 3
f. The real numbers are 25, , −15, − , 5. The real numbers are {all numbers that
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3 4 correspond to points on a number line}.
5, −3.7, 8.8, −99.
6. The rational numbers are
6. a. 0 < 3 since 0 is to the left of 3 on a number a
line. a and b are integers, b ≠ 0 .
b
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b. 15 > −5 since 15 is to the right of −5 on a
7. The irrational numbers are {nonrational numbers
number line.
that correspond to points on a number line}.
Copyright © 2023 Pearson Education, Inc. 1
, Chapter 1: Review of Real Numbers ISM: Beginning Algebra
8. The distance between a number b and 0 on a 28. Negative seven is not equal to seven is written as
number line is |b|. −7 ≠ 7.
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9. To form a true statement: 0 < 7. 30. The integer 535 represents 535 feet above sea
level. The integer −8 represents 8 feet below sea
10. Five is greater than or equal to four; 5 ≥ 4 level.
11. 0 belongs to the whole numbers, the integers, the 32. The integer −11,496 represents 11,496 fewer
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rational numbers, and the real numbers; since 0 students.
is a rational number, it cannot also be an
irrational number. 34. 30 represents an ascent of feet. −50 represents a
descent of 50 feet.
12. The absolute value of a real number a, denoted
by |a|, is the distance between a and 0 on a 1
number line. 36. The number belongs to the sets of: rational
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4
Exercise Set 1.2 numbers and real numbers.
2. 9 < 15 since 9 is to the left of 15 on a number 1
38. The number − belongs to the sets of: rational
line. 2
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numbers and real numbers.
4. 2.13 > 1.13 since 2.13 is to the right of 1.13 on a
number line. 40. The number 5 belongs to the sets of: natural
numbers, whole numbers, integers, rational
6. 20 > 0 since 20 is to the right of 0 on a number numbers, and real numbers.
line.
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42. The number 3 belongs to the sets of: irrational
8. −4 > −6 since −4 is to the right of −6 on a numbers and real numbers.
number line.
5
10. 0 < 100 since 0 is to the left of 100 on a number 44. The number −1 belongs to the sets of: rational
line. 9
numbers and real numbers.
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12. 360 ≥ 180 since 360 is to the right of 180 on a
number line. 46. False; negative numbers may be irrational.
14. 4 ≥ 7 is false, since 4 is to the left of 7 on a 48. True
number line.
50. False; irrational numbers are real.
16. 17 > 16 is true, since 17 is to the right of 16 on a
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number line. 1
52. False; is not an integer.
2
18. 8 ⋅ 8 ≤ 8 ⋅ 7 is false, since 56 is to the left of 64
on a number line. 54. False; 0 is a whole number that is not positive.
20. 4 < 7 is true, since 4 is to the left of 7 on a 56. −200 < −20 since −200 is to the left of −20 on a
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number line. number line.
22. 0 < −15 is false, since 0 is to the right of −15 on 58. 7.1 > −7 since 7.1 is to the right of −7 on a
a number line. number line.
24. Fifteen is greater than five is written as 15 > 5. 18 24
60. < since 6 < 8.
??
3 3
26. Negative ten is less than or equal to thirty-seven
is written as −10 ≤ 37. 62. |−20| > −200 since 20 > 200.
2 Copyright © 2023 Pearson Education, Inc.
ST
SOLUTIONS
UV
MANUAL
IA
_A
Elayn Martin-Gay
PP
Comprehensive Solutions Manual for Instructors and
RO
Students
© Elayn Martin-Gay
VE
All rights reserved. Reproduction or distribution without permission is prohibited.
D?
??
©STUDYSTREAM
, Contents
ST
UV
Chapter 1 1
Chapter 2 34
IA
Chapter 3 104
Chapter 4 160
_A
Chapter 5 212
Chapter 6 253
PP
Chapter 7 295
Chapter 8 368
RO
Chapter 9 410
Appendix A 467
Appendix B 469
VE
Appendix C 471
Appendix D 473
D?
Practice Final Exam 475
??
, Chapter 1
ST
Section 1.2 Practice Exercises 12 12
c. 3= since simplifies to 3.
4 4
1. a. 5 < 8 since 5 is to the left of 8 on the number
line. 7. a. |−8| = 8 since −8 is 8 units from 0 on a
number line.
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b. 6 > 4 since 6 is to the right of 4 on the
number line. b. |9| = 9 since 9 is 9 units from 0 on a number
line.
c. 16 < 82 since 16 is to the left of 82 on the
number line.
c. |−2.5| = 2.5 since −2.5 is 2.5 units from 0 on
a number line.
2. a. 9 ≥ 3 is true, since 9 > 3 is true.
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b. 3 ≥ 8 is false, since neither 3 > 8 nor 3 = 8 is 5 5 5 5
d. = since is unit from 0 on a
true. 11 11 11 11
number line.
c. 25 ≤ 25 is true, since 25 = 25 is true.
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1 1 1 1
d. 4 ≤ 14 is true, since 4 < 14 is true. e. − = since − is unit from 0 on a
2 2 2 2
3. a. 3<8 number line.
b. 15 ≥ 9 8. a. |8| = |−8| since 8 = 8.
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c. 6≠7 b. |−3| > 0 since 3 > 0.
4. The integer −10 represents 10 meters below sea c. |−7| < |−11| since 7 < 11.
level.
d. |3| > |2| since 3 > 2.
5. a. The natural number is 25.
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e. |0| < |−4| since 0 < 4.
b. The whole number is 25.
Vocabulary, Readiness & Video Check 1.2
c. The integers are 25, −15, −99.
1. The whole numbers are {0, 1, 2, 3, 4, ...}.
7 3 2. The natural numbers are {1, 2, 3, 4, 5, ...}.
d. The rational numbers are 25, , −15, − ,
3 4
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−3.7, 8.8, −99. 3. The symbols ≠, ≤, and > are called inequality
symbols.
e. The irrational number is 5.
4. The integers are {..., −3, −2, −1, 0, 1, 2, 3, ...}.
7 3
f. The real numbers are 25, , −15, − , 5. The real numbers are {all numbers that
D?
3 4 correspond to points on a number line}.
5, −3.7, 8.8, −99.
6. The rational numbers are
6. a. 0 < 3 since 0 is to the left of 3 on a number a
line. a and b are integers, b ≠ 0 .
b
??
b. 15 > −5 since 15 is to the right of −5 on a
7. The irrational numbers are {nonrational numbers
number line.
that correspond to points on a number line}.
Copyright © 2023 Pearson Education, Inc. 1
, Chapter 1: Review of Real Numbers ISM: Beginning Algebra
8. The distance between a number b and 0 on a 28. Negative seven is not equal to seven is written as
number line is |b|. −7 ≠ 7.
ST
9. To form a true statement: 0 < 7. 30. The integer 535 represents 535 feet above sea
level. The integer −8 represents 8 feet below sea
10. Five is greater than or equal to four; 5 ≥ 4 level.
11. 0 belongs to the whole numbers, the integers, the 32. The integer −11,496 represents 11,496 fewer
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rational numbers, and the real numbers; since 0 students.
is a rational number, it cannot also be an
irrational number. 34. 30 represents an ascent of feet. −50 represents a
descent of 50 feet.
12. The absolute value of a real number a, denoted
by |a|, is the distance between a and 0 on a 1
number line. 36. The number belongs to the sets of: rational
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4
Exercise Set 1.2 numbers and real numbers.
2. 9 < 15 since 9 is to the left of 15 on a number 1
38. The number − belongs to the sets of: rational
line. 2
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numbers and real numbers.
4. 2.13 > 1.13 since 2.13 is to the right of 1.13 on a
number line. 40. The number 5 belongs to the sets of: natural
numbers, whole numbers, integers, rational
6. 20 > 0 since 20 is to the right of 0 on a number numbers, and real numbers.
line.
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42. The number 3 belongs to the sets of: irrational
8. −4 > −6 since −4 is to the right of −6 on a numbers and real numbers.
number line.
5
10. 0 < 100 since 0 is to the left of 100 on a number 44. The number −1 belongs to the sets of: rational
line. 9
numbers and real numbers.
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12. 360 ≥ 180 since 360 is to the right of 180 on a
number line. 46. False; negative numbers may be irrational.
14. 4 ≥ 7 is false, since 4 is to the left of 7 on a 48. True
number line.
50. False; irrational numbers are real.
16. 17 > 16 is true, since 17 is to the right of 16 on a
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number line. 1
52. False; is not an integer.
2
18. 8 ⋅ 8 ≤ 8 ⋅ 7 is false, since 56 is to the left of 64
on a number line. 54. False; 0 is a whole number that is not positive.
20. 4 < 7 is true, since 4 is to the left of 7 on a 56. −200 < −20 since −200 is to the left of −20 on a
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number line. number line.
22. 0 < −15 is false, since 0 is to the right of −15 on 58. 7.1 > −7 since 7.1 is to the right of −7 on a
a number line. number line.
24. Fifteen is greater than five is written as 15 > 5. 18 24
60. < since 6 < 8.
??
3 3
26. Negative ten is less than or equal to thirty-seven
is written as −10 ≤ 37. 62. |−20| > −200 since 20 > 200.
2 Copyright © 2023 Pearson Education, Inc.
