,Solution manual for College Algebra, 13th Edition
R. David Gustafson
Notes
1- All Chapters are step by step.
2- We have shown you 10 pages.
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:
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
Solution and Answer Guide
GUSTAFSON/HUGHES, C OLLEGE ALGEBRA 2023, 9780357723654; C HAPTER R: A REVIEW OF
BASIC ALGEBRA
TABLE OF CONTENTS
End of Section Exercise Solutions ....................................................................................... 1
Exercises R.1 ..................................................................................................................................1
Exercises R.2 .............................................................................................................................. 19
Exercises R.3 ..............................................................................................................................43
Exercises R.4 ............................................................................................................................. 66
Exercises R.5 ..............................................................................................................................92
Exercises R.6 ............................................................................................................................. 115
Chapter Review Solutions................................................................................................ 144
Chapter Test Solutions .................................................................................................... 167
Group Activity Solutions ...................................................................................................175
END OF SECTION EXERCISE SOLUTIONS
EXERCISES R.1
Getting Ready
Complete these just-in-time review problems to prepare you to successfully work the
practice exercises.
1. Simplify. 10 – 20
Solution
10 20 10
2. Simplify. 5 – (–10)
Solution
5 10 15
3. Division by what number is undefined?
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
1
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
Solution
Division by 0 is undefined
5 0 0
4. Given , , and . Which one is equivalent to 0?
0 5 0
Solution
0
0
5
5. Write the inequality symbol for greater than.
Solution
The inequality symbol for greater than is >
6. Write the math symbol for infinity.
Solution
The math symbol for infinity is
Vocabulary and Concepts
You should be able to complete these vocabulary and concept statements before you proceed
to the practice exercises.
Fill in the blanks.
7. A ______ is a collection of objects.
Solution
set
8. If every member of one set B is also a member of a second set A, then B is called a
________ of A.
Solution
subset
9. If A and B are two sets, the set that contains all members that are in sets A and B or
both is called the ________ of A and B.
Solution
union
10. If A and B are two sets, the set that contains all members that are in both sets is
called the ________of A and B.
Solution
intersection
11. A real number is any number that can be expressed as a __________ .
Solution
decimal
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
2
website, in whole or in part.
,Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
12. A __________ is a letter that is used to represent a number.
Solution
variable
13. The smallest prime number is __________.
Solution
2
14. All integers that are exactly divisible by 2 are called _________integers.
Solution
even
15. Natural numbers greater than 1 that are not prime are called __________numbers.
Solution
composite
16. Fractions such as 2
3
, 82 , and 97 are called _________ numbers.
Solution
rational
17. Irrational numbers are ________ that don’t terminate and don’t repeat.
Solution
decimals
18. The symbol ________is read as “is less than or equal to.”
Solution
19. On a number line, the __________ numbers are to the left of 0.
Solution
negative
20. The only integer that is neither positive nor negative is _________.
Solution
0
21. The Associative Property of Addition states that x y z _________.
Solution
x y z
22. The Commutative Property of Multiplication states that xy = __________.
Solution
yx
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
3
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
23. Use the Distributive Property to complete the statement: 5(m + 2) = ___________.
Solution
5m 5 2
24. The statement (m + n) p = p(m + n) illustrates the __________ Property of ________.
Solution
Commutative, Multiplication
25. The graph of an __________ is a portion of a number line.
Solution
interval
26. The graph of an open interval has _________ endpoints.
Solution
no
27. The graph of a closed interval has __________ endpoints.
Solution
two
28. The graph of a _________ interval has one endpoint.
Solution
half-open
29. Except for 0, the absolute value of every number is _________.
Solution
positive
30. The __________ between two distinct points on a number line is always positive.
Solution
distance
Let
N = the set of natural numbers
W = the set of whole numbers
Z = the set of integers
Q = the set of rational numbers
R = the set of real numbers
Determine whether each statement is true or false. Read the symbol , as “is a subset of.”
31. N W
Solution
Every natural number is a whole number, so N W. TRUE
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
4
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
32. Q R
Solution
Every rational number is a real number, so Q R. TRUE
33. Q N
Solution
The rational number 1
2
is not a natural number, so Q | N. FALSE
34. Z Q
Solution
Every integer is a rational number, so Z Q. TRUE
35. W Z
Solution
Every whole number is an integer, so W Z. TRUE
36. R Z
Solution
The real number 2 is not an integer, so R | Z FALSE
Practice
L
e
t
=
a
,
b
,
c
,
d
,
e
=
d
,
e
,
f
,
g
a
n
d
=
a
,
c
,
e
,
f
A , B , C . Find each set.
37. A B
Solution
A B {a, b, c, d, e, f, g}
38. A B
Solution
A B {d, e}
39. A C
Solution
A C {a, c, e}
40. B C
Solution
B C {a, c, d, e, f, g}
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
5
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
Determine whether the decimal form of each fraction terminates or repeats.
7
41.
16
Solution
7
0.4375; terminates
16
5
42.
8
Solution
5
0.625; terminates
8
5
43.
11
Solution
5
= 0.454545...; repeats
11
7
44.
12
Solution
7
0.583333...; repeats
12
Consider the following set:
5
,
4
,
,
0
,
1
,
2
,
2
,
2
.
7
5
,
6
,
7
23
45. Which numbers are natural numbers?
Solution
natural: 1, 2, 6, 7
46. Which numbers are whole numbers?
Solution
whole: 0, 1, 2, 6, 7
47. Which numbers are integers?
Solution
integers: –5, –4, 0, 1, 2, 6, 7
48. Which numbers are rational numbers?
Solution
rational: 5, 4, 23 , 0, 1, 2, 2.75, 6, 7
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
6
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
49. Which numbers are irrational numbers?
Solution
irrational: 2
50. Which numbers are prime numbers?
Solution
prime: 2,7
51. Which numbers are composite numbers?
Solution
composite: 6
52. Which numbers are even integers?
Solution
even: –4, 0, 2, 6
53. Which numbers are odd integers?
Solution
odd: –5, 1, 7
54. Which numbers are negative numbers?
Solution
negative: 5, 4, 23
Graph each subset of the real numbers on a number line.
55. The natural numbers between 1 and 5
Solution
56. The composite numbers less than 10
Solution
57. The prime numbers between 10 and 20
Solution
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
7
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
58. The integers from –2 to 4
Solution
59. The integers between –5 and 0
Solution
60. The even integers between –9 and –1
Solution
61. The odd integers between –6 and 4
Solution
62. 0.7, 1.75, and 3 87
Solution
Write each inequality in interval notation and graph the interval.
63. x 2
Solution
x 2 2,
64. x 4
Solution
x 4 , 4
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
8
website, in whole or in part.
R. David Gustafson
Notes
1- All Chapters are step by step.
2- We have shown you 10 pages.
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:
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
Solution and Answer Guide
GUSTAFSON/HUGHES, C OLLEGE ALGEBRA 2023, 9780357723654; C HAPTER R: A REVIEW OF
BASIC ALGEBRA
TABLE OF CONTENTS
End of Section Exercise Solutions ....................................................................................... 1
Exercises R.1 ..................................................................................................................................1
Exercises R.2 .............................................................................................................................. 19
Exercises R.3 ..............................................................................................................................43
Exercises R.4 ............................................................................................................................. 66
Exercises R.5 ..............................................................................................................................92
Exercises R.6 ............................................................................................................................. 115
Chapter Review Solutions................................................................................................ 144
Chapter Test Solutions .................................................................................................... 167
Group Activity Solutions ...................................................................................................175
END OF SECTION EXERCISE SOLUTIONS
EXERCISES R.1
Getting Ready
Complete these just-in-time review problems to prepare you to successfully work the
practice exercises.
1. Simplify. 10 – 20
Solution
10 20 10
2. Simplify. 5 – (–10)
Solution
5 10 15
3. Division by what number is undefined?
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
1
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
Solution
Division by 0 is undefined
5 0 0
4. Given , , and . Which one is equivalent to 0?
0 5 0
Solution
0
0
5
5. Write the inequality symbol for greater than.
Solution
The inequality symbol for greater than is >
6. Write the math symbol for infinity.
Solution
The math symbol for infinity is
Vocabulary and Concepts
You should be able to complete these vocabulary and concept statements before you proceed
to the practice exercises.
Fill in the blanks.
7. A ______ is a collection of objects.
Solution
set
8. If every member of one set B is also a member of a second set A, then B is called a
________ of A.
Solution
subset
9. If A and B are two sets, the set that contains all members that are in sets A and B or
both is called the ________ of A and B.
Solution
union
10. If A and B are two sets, the set that contains all members that are in both sets is
called the ________of A and B.
Solution
intersection
11. A real number is any number that can be expressed as a __________ .
Solution
decimal
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
2
website, in whole or in part.
,Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
12. A __________ is a letter that is used to represent a number.
Solution
variable
13. The smallest prime number is __________.
Solution
2
14. All integers that are exactly divisible by 2 are called _________integers.
Solution
even
15. Natural numbers greater than 1 that are not prime are called __________numbers.
Solution
composite
16. Fractions such as 2
3
, 82 , and 97 are called _________ numbers.
Solution
rational
17. Irrational numbers are ________ that don’t terminate and don’t repeat.
Solution
decimals
18. The symbol ________is read as “is less than or equal to.”
Solution
19. On a number line, the __________ numbers are to the left of 0.
Solution
negative
20. The only integer that is neither positive nor negative is _________.
Solution
0
21. The Associative Property of Addition states that x y z _________.
Solution
x y z
22. The Commutative Property of Multiplication states that xy = __________.
Solution
yx
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
3
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
23. Use the Distributive Property to complete the statement: 5(m + 2) = ___________.
Solution
5m 5 2
24. The statement (m + n) p = p(m + n) illustrates the __________ Property of ________.
Solution
Commutative, Multiplication
25. The graph of an __________ is a portion of a number line.
Solution
interval
26. The graph of an open interval has _________ endpoints.
Solution
no
27. The graph of a closed interval has __________ endpoints.
Solution
two
28. The graph of a _________ interval has one endpoint.
Solution
half-open
29. Except for 0, the absolute value of every number is _________.
Solution
positive
30. The __________ between two distinct points on a number line is always positive.
Solution
distance
Let
N = the set of natural numbers
W = the set of whole numbers
Z = the set of integers
Q = the set of rational numbers
R = the set of real numbers
Determine whether each statement is true or false. Read the symbol , as “is a subset of.”
31. N W
Solution
Every natural number is a whole number, so N W. TRUE
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
4
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
32. Q R
Solution
Every rational number is a real number, so Q R. TRUE
33. Q N
Solution
The rational number 1
2
is not a natural number, so Q | N. FALSE
34. Z Q
Solution
Every integer is a rational number, so Z Q. TRUE
35. W Z
Solution
Every whole number is an integer, so W Z. TRUE
36. R Z
Solution
The real number 2 is not an integer, so R | Z FALSE
Practice
L
e
t
=
a
,
b
,
c
,
d
,
e
=
d
,
e
,
f
,
g
a
n
d
=
a
,
c
,
e
,
f
A , B , C . Find each set.
37. A B
Solution
A B {a, b, c, d, e, f, g}
38. A B
Solution
A B {d, e}
39. A C
Solution
A C {a, c, e}
40. B C
Solution
B C {a, c, d, e, f, g}
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
5
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
Determine whether the decimal form of each fraction terminates or repeats.
7
41.
16
Solution
7
0.4375; terminates
16
5
42.
8
Solution
5
0.625; terminates
8
5
43.
11
Solution
5
= 0.454545...; repeats
11
7
44.
12
Solution
7
0.583333...; repeats
12
Consider the following set:
5
,
4
,
,
0
,
1
,
2
,
2
,
2
.
7
5
,
6
,
7
23
45. Which numbers are natural numbers?
Solution
natural: 1, 2, 6, 7
46. Which numbers are whole numbers?
Solution
whole: 0, 1, 2, 6, 7
47. Which numbers are integers?
Solution
integers: –5, –4, 0, 1, 2, 6, 7
48. Which numbers are rational numbers?
Solution
rational: 5, 4, 23 , 0, 1, 2, 2.75, 6, 7
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
6
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
49. Which numbers are irrational numbers?
Solution
irrational: 2
50. Which numbers are prime numbers?
Solution
prime: 2,7
51. Which numbers are composite numbers?
Solution
composite: 6
52. Which numbers are even integers?
Solution
even: –4, 0, 2, 6
53. Which numbers are odd integers?
Solution
odd: –5, 1, 7
54. Which numbers are negative numbers?
Solution
negative: 5, 4, 23
Graph each subset of the real numbers on a number line.
55. The natural numbers between 1 and 5
Solution
56. The composite numbers less than 10
Solution
57. The prime numbers between 10 and 20
Solution
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
7
website, in whole or in part.
, Solution and Answer Guide: Gustafson/Hughes, College Algebra 2023, 9780357723654; Chapter R: A Review of Basic Algebra
58. The integers from –2 to 4
Solution
59. The integers between –5 and 0
Solution
60. The even integers between –9 and –1
Solution
61. The odd integers between –6 and 4
Solution
62. 0.7, 1.75, and 3 87
Solution
Write each inequality in interval notation and graph the interval.
63. x 2
Solution
x 2 2,
64. x 4
Solution
x 4 , 4
© 2022 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
8
website, in whole or in part.
