solutions
Beginning &
Intermediate
?M
Algebra, 7th edition
ED
Authors:
Elayn Martin-Gay
GE
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, Chapter 1
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.
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.
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
ED
3. a. 3<8 number line.
b. 15 ≥ 9 8. a. |8| = |−8| since 8 = 8.
c. 6≠7 b. |−3| > 0 since 3 > 0.
GE
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.
e. |0| < |−4| since 0 < 4.
EK
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
d. The rational numbers are 25, , −15, − , 2. The natural numbers are {1, 2, 3, 4, 5, ...}.
??
3 4
−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
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
number line. 7. The irrational numbers are {nonrational numbers
that correspond to points on a number line}.
Copyright © 2023 Pearson Education, Inc. 1
,Chapter 1: Review of Real Numbers ISM: Beginning and Intermediate 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.
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
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
4
?M
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
numbers and real numbers.
4. 2.13 > 1.13 since 2.13 is to the right of 1.13 on a
ED
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.
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.
GE
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.
12. 360 ≥ 180 since 360 is to the right of 180 on a
EK
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
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
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.
, ISM: Beginning and Intermediate Algebra Chapter 1: Review of Real Numbers
64. 0 = |0| since 0 = 0. 63 3⋅3⋅ 7 7 7
2. a. = = =
72 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 2 ⋅ 2 ⋅ 2 8
2 2 2 2
66. = − since = .
5 5 5 5 64 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 2 ⋅ 2 ⋅ 2 ⋅ 2 16
b. = = =
12 2⋅2⋅3 3 3
68. −500 < |−50| since −500 < 50.
7 7
24 24 c. =
70. −12 = since 12 = . 25 5 ⋅ 5
2 2 There are no common factors other than 1,
72. The 2020 blueberry production in Michigan was 7
so is already in lowest terms.
74 million pounds, while the 2020 blueberry 25
production in Washington was 168 million
pounds. 3 7 3⋅7 3⋅7 7 7
3. ⋅ = = = =
74 million < 168 million
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8 9 8 ⋅ 9 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 2 ⋅ 2 ⋅ 2 ⋅ 3 24
74. The 2020 blueberry production in Oregon was 3 4 3 9 3 ⋅ 9 27
154 million pounds, while the 2020 blueberry 4. a. ÷ = ⋅ = =
4 9 4 4 4 ⋅ 4 16
production in Washington was 168 million
pounds.
5 5 1 5 ⋅1 5 1
168 − 154 = 14 b. ÷ 15 = ⋅ = = =
ED
The production in Oregon was 14 million pounds 12 12 15 12 ⋅ 15 12 ⋅ 3 ⋅ 5 36
less or −14 million.
7 7 7 15 7 ⋅ 15 15 3 ⋅ 5 5
c. ÷ = ⋅ = = = =
76. The tallest bar represents 55 players admitted. 6 15 6 7 6⋅7 6 2⋅3 2
78. Look for the bars that have heights less than 30; 8 3 8−3 5
GE
1931−1940 and 1951−1960. 5. a. − = = =1
5 5 5 5
80. answers may vary
8 2 8−2 6
b. − = =
82. 0.96 < 0.98 since 0.96 is to the left of 0.98 on the 5 5 5 5
number line.
EK
3 1 3 +1 4
84. Spica is dimmer since 0.98 > 0.96. c. + = =
5 5 5 5
86. Regulus is dimmest since 1.35 is to the right of
all other numbers listed. 5 1 5 +1 6 1
d. + = = =
??
12 12 12 12 2
88. 13 ≥ −13 has the same meaning as −13 ≤ 13.
2 2 7 2 ⋅ 7 14
90. 73 < 75 has the same meaning as 75 > 73. 6. = ⋅ = =
3 3 7 3 ⋅ 7 21
92. −2 > −4 has the same meaning as −4 < −2. 5 1 5 ⋅ 7 1 ⋅ 11
7. a. + = +
94. answers may vary 11 7 11 ⋅ 7 7 ⋅ 11
35 11
= +
Section 1.3 Practice Exercises 77 77
35 + 11
1. a. 36 = 4 ⋅ 9 = 2 ⋅ 2 ⋅ 3 ⋅ 3 =
77
46
b. 200 = 2 ⋅100 = 2 ⋅ 4 ⋅ 25 = 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5 =
77
Copyright © 2023 Pearson Education, Inc. 3
Beginning &
Intermediate
?M
Algebra, 7th edition
ED
Authors:
Elayn Martin-Gay
GE
◊ All CHAPtERs
EK
◊ instAnt PDF DoWnloAD💯💯💯
◊ oRiGinAl FRoM PuBlisHER
??
MEDGEEK
Email:
, Chapter 1
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.
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.
?M
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.
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
ED
3. a. 3<8 number line.
b. 15 ≥ 9 8. a. |8| = |−8| since 8 = 8.
c. 6≠7 b. |−3| > 0 since 3 > 0.
GE
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.
e. |0| < |−4| since 0 < 4.
EK
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
d. The rational numbers are 25, , −15, − , 2. The natural numbers are {1, 2, 3, 4, 5, ...}.
??
3 4
−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
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
number line. 7. The irrational numbers are {nonrational numbers
that correspond to points on a number line}.
Copyright © 2023 Pearson Education, Inc. 1
,Chapter 1: Review of Real Numbers ISM: Beginning and Intermediate 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.
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
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
4
?M
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
numbers and real numbers.
4. 2.13 > 1.13 since 2.13 is to the right of 1.13 on a
ED
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.
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.
GE
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.
12. 360 ≥ 180 since 360 is to the right of 180 on a
EK
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
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
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.
, ISM: Beginning and Intermediate Algebra Chapter 1: Review of Real Numbers
64. 0 = |0| since 0 = 0. 63 3⋅3⋅ 7 7 7
2. a. = = =
72 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 2 ⋅ 2 ⋅ 2 8
2 2 2 2
66. = − since = .
5 5 5 5 64 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 2 ⋅ 2 ⋅ 2 ⋅ 2 16
b. = = =
12 2⋅2⋅3 3 3
68. −500 < |−50| since −500 < 50.
7 7
24 24 c. =
70. −12 = since 12 = . 25 5 ⋅ 5
2 2 There are no common factors other than 1,
72. The 2020 blueberry production in Michigan was 7
so is already in lowest terms.
74 million pounds, while the 2020 blueberry 25
production in Washington was 168 million
pounds. 3 7 3⋅7 3⋅7 7 7
3. ⋅ = = = =
74 million < 168 million
?M
8 9 8 ⋅ 9 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3 2 ⋅ 2 ⋅ 2 ⋅ 3 24
74. The 2020 blueberry production in Oregon was 3 4 3 9 3 ⋅ 9 27
154 million pounds, while the 2020 blueberry 4. a. ÷ = ⋅ = =
4 9 4 4 4 ⋅ 4 16
production in Washington was 168 million
pounds.
5 5 1 5 ⋅1 5 1
168 − 154 = 14 b. ÷ 15 = ⋅ = = =
ED
The production in Oregon was 14 million pounds 12 12 15 12 ⋅ 15 12 ⋅ 3 ⋅ 5 36
less or −14 million.
7 7 7 15 7 ⋅ 15 15 3 ⋅ 5 5
c. ÷ = ⋅ = = = =
76. The tallest bar represents 55 players admitted. 6 15 6 7 6⋅7 6 2⋅3 2
78. Look for the bars that have heights less than 30; 8 3 8−3 5
GE
1931−1940 and 1951−1960. 5. a. − = = =1
5 5 5 5
80. answers may vary
8 2 8−2 6
b. − = =
82. 0.96 < 0.98 since 0.96 is to the left of 0.98 on the 5 5 5 5
number line.
EK
3 1 3 +1 4
84. Spica is dimmer since 0.98 > 0.96. c. + = =
5 5 5 5
86. Regulus is dimmest since 1.35 is to the right of
all other numbers listed. 5 1 5 +1 6 1
d. + = = =
??
12 12 12 12 2
88. 13 ≥ −13 has the same meaning as −13 ≤ 13.
2 2 7 2 ⋅ 7 14
90. 73 < 75 has the same meaning as 75 > 73. 6. = ⋅ = =
3 3 7 3 ⋅ 7 21
92. −2 > −4 has the same meaning as −4 < −2. 5 1 5 ⋅ 7 1 ⋅ 11
7. a. + = +
94. answers may vary 11 7 11 ⋅ 7 7 ⋅ 11
35 11
= +
Section 1.3 Practice Exercises 77 77
35 + 11
1. a. 36 = 4 ⋅ 9 = 2 ⋅ 2 ⋅ 3 ⋅ 3 =
77
46
b. 200 = 2 ⋅100 = 2 ⋅ 4 ⋅ 25 = 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5 =
77
Copyright © 2023 Pearson Education, Inc. 3
