Beginning and Intermediate Algebra (2nd Edition) pot
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1
Beginning and Intermediate Algebra
Student Solutions Manual
Complete worked solutions to odd problems
Solutions manual has not been cross checked for accuracy.
If you disagree with this solutions manual you should check with your instructor.
Should you find an error, please E-mail
so it can be corrected.
Thank you!
Beginning Algebra Student Solutions Manual by Tyler Wallace is licensed under a
Creative Commons Attribution 3.0 Unported License. Permissions beyond the scope of
this license may be available at
2
Beginning and Intermediate Algebra
Student Solutions Manual Table of Contents
Chapter 0: Arithmetic 3
Chapter 1: Solving Linear Equations 11
Chapter 2: Graphing Linear Equations 40
Chapter 3: Inequalities 55
Chapter 4: Systems of Equations 62
Chapter 5: Polynomials 88
Chapter 6: Factoring 99
Chapter 7: Rational Expressions 109
Chapter 8: Radical Expressions 130
Chapter 9: Quadratics 144
Chapter 10: Functions 189
3
Chapter 0: Arithmetic
4
0.1
1) 1 3
1
3
2
3)
6
8
6 82
5)
3
3
3
3
6
7) 35
358
9)
7
5
7 52
11) 31
314
13) 63
633
15)
5
32
17) 23
2
3
1
19)
8
5
8 53
21)
2
5
7
23) 56
5611
25) 6 33
27) 47
4
7
3
29)
7
70
31)
4
1
4
33)
10
8
80
35)
4
2
8
37)
7
8
56
39)
9
4
36
41)
5
2
10
43)
5
4
20
45)
4
6
24
47)
7
49)
2
51)
2
53)
7
55)
4
57)
8
59)
6
0.2
1)
3)
5)
7)
9)
11)
13)
15)
17)
19)
21)
·
8
23)
·
25)
2
27)
29)
4
1
1
-1
4
-3
4
4
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1 2
5
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33)
3
35)
37)
39)
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43)
45)
47)
49)
51)
53)
1
55)
57)
3
59)
61)
63)
65)
67)
1
69)
71)
73)
75)
77)
79)
81)
2
0.3
1) 6 · 41
241
24
3) 38
|
4
|
384
32
5
5) 84·2
2·2
4
7) 9 2 5 6
9
3
6
6 6
1
1
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1
5
6
9) 6
3 3
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3
6 36 3
6 12
6
11) 42
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16
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46
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2
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6
5
12 2
6
5
|
3
|
14
6
5
3
202
40
19)
: 132
15
: 2
1
6
1
3
2
1
6
2
21
6
2
3
6
2
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3
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4
4
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1
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15
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4
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5
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4
84
12
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4
5
1
5
186
4
5
5
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4
25
24
4
25
28 25
3
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4
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|
|
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246·2
59246·2
594·2
598
14 8
6
:
53
2
5
|
2
5
|
53
45
|
45
|
53
1
|
1
|
53
1
2
1
21
3
:
2
8
0.4
1) 1 , 1,3,4
3
1
4
1
4
4
1
81
7
3)
, 6,5
6
6
5
1
5)
1
, 3,5
5
3
1
5
2
25 2
23
7) 5
, 5,4,2
5
4
5
4
5
20 5
25
9)
, 4,6,6
6
6
6
167
11)
, 1,2
1
2
1
1
2
1
1
3
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1
41
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13)
13
, 3,6
6
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6
13
6
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53
6
3
2
32
1
15)
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, 3,
1,6
1
4
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1
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1
3
1
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3
1
0
1
17) 3
5, 4,5
5
3
4
5
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5
3
9
5
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9
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9
5
36 5
31
19)
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6
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42
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15
11
Chapter 1: Solving Linear Equations
12
1.1
1) 916
9 9
7
3) 1116
11 11
5
5) 30 20
20 20
10
7) 726
7 7
19
9) 13 5
5 5
18
11)
20
13)
12
9
12
108
15)
8
17)
17
19)
20
21) 16 13
16 16
3
23) 821
8 8
13
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15
27)
10
29)
14
14
5
31) 74
4 4
11
33) 10 4
4 4
14
35)
11
37)
20
1220
240
39) 9 7
9 9
16
1.2
1) 5
4
5 5
4
14
4
3) 1027 4
4 4
7/7
14
5) 8 377
3 3
10
7)
0
9) 8
6
6 6
5
2
5
10
11) 07
7 7
2
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2
14
13) 12 30
12 12
4
13
15) 242 8
8 8
16
17) 212 2
12 12
7
19)
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7 7
3
33
9
21) 1528 64
64 64
11
23) 168 64
64 64
10
25) 56 864
56 56
1
27) 2 422
4 4
9
29) 204 4
4 4
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31) 53
3 3
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8
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6 6
8
18
8
35) 404 32
32 32
2
37) 873 7
3 3
12
39) 111
1 1
12
1.3
1) 2
3 8
1
2 3 81
10 31
10 10
3
3) 5
4 2
50
20 1050
20 20
7
5) 6666 5
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36 36
1
7) 08 5
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14
9) 2 2
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16
2 16 1416
16 1616
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11) 211263
21 21
126 18
6 6
1
13) 1 78 7
8 8
1 7
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15) 1 1229 8
12 12
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29 29
7
17) 20 712 30
12 12
20 530
20 20
2
19) 32 2434 2
24 24
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3
21) 2 5
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2 10 20335
12 2033 5
5 5
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23) 4 112
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3
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6 294 5 5
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1)
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12 12
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25)
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24 24
454 19
19 19
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27)
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21 21
39 2738
27 27
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18
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27 27
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30 30
1.5
1)
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7)
2
2 3 3
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6 3 3 2
2 9 3 6
18
9)
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3
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2 2
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25)
27) 16
16
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6
6
4 4 4 109 12
105 12 9 9
12 12 13 1012
10 10
,
1.7
1) c varies directly as a
3) w varies inversely as x
5) f varies jointly as x and y
7) h is directly proportional to b
9) a is inversely proportional to b
22
11) p is jointly proportional to q and r and p = 12 when q = 8 and r = 3
13) t varies directly as the square of u and t = 6 when u = 3
15) w is inversely proportional to the cube of x and w is 54 when x = 3
54
3
54
27
1458
17) a is jointly proportional with the square of x and the square root of y and
a = 25 when x = 5 and y = 9
√
·
19) The electrical current, in amperes, in a circuit varies directly as the voltage. When 15 volts are
applied, the current is 5 amperes. What is the current when 18 volts are applied?
18
18
6
21) Hooke’s law states that the distance that a spring is stretched by hanging object varies directly as
the mass of the object. If the distance is 20 cm when the mass is 3 kg, what is the distance when
the mass is 5 kg?
33.3 .
23
23) The number of aluminum cans used each year varies directly as the number of people using the
cans. If 250 people use 60,000 cans in one year, how many cans are used each year in Dallas,
which has a population of 1,008,000?
250
1,000,000
,,
240 1,000,000
241,920,000
25) According to Fidelity Investment Vision Magazine, the average weekly allowance of children varies
directly as their grade level. In a recent year, the average allowance of a 9th-grade student was
9.66 dollars per week. What was the average weekly allowance of a 4th-grade student?
.
1.07
4
1.074
$4.28
27) The number of kilograms of water in a human body varies directly as the mass of the body. A 96-
kg person contains 64 kg of water. How many kilo grams of water are in a 60-kg person?
60
60
40
29) The weight of an object on Mars varies directly as its weight on Earth. A person weighs 95lb on
Earth weighs 38 lb on Mars. How much would a 100-lb person weigh on Mars?
100
100
40
31) The time required to empty a tank varies inversely as the rate of pumping. If a pump can empty a
tank in 45 min at the rate of 600 kL/min, how long will it take the pump to empty the same tank at
the rate of 1000 kL/min?
45
600
27000
27
24
33) The stopping distance of a car after the brakes have been applied varies directly as the square of
the speed r. If a car, traveling 60 mph can stop in 200 ft, how fast can a car go and still stop in 72
ft?
18
72
18
√
1296
√
36
35) The intensity of a light from a light bulb varies inversely as the square of the distance from the
bulb. Suppose intensity is 90 W/
(watts per square meter) when the distance is 5 m. How much
further would it be to a point where the intensity is 40 W/
?
90
5
90
25
2250
√
√
56.25
7.5
7.5 52.5
37) The intensity of a television signal varies inversely as the square of the distance from the
transmitter. If the intensity is 25 W/
at a distance of 2 km, how far from the transmitter are
you when the intensity is 2.56 W/
?
25
2
25
4
100
.
.
.
√
√
39.0625
6.25
1.8
1) When five is added to three more than a certain number, the result is 19. What is the number?
3519
819
8 8
11
25
3) When 18 is subtracted from six times a certain number, the result is − 42. What is the number?
6 1842
18 18
4
5) A number plus itself, plus twice itself, plus 4 times itself, is equal to − 104. What is the number?
2 4104
13
7) Eleven less than seven times a number is five more than six times the number. Find the number.
7 116 5
6 6
115
11 11
16
9) The sum of three consecutive integers is 108. What are the integers?
:
: 1
:2
3 3108
3 3
35 35,36,37
11) Find three consecutive integers such that the sum of the first, twice the second, and three times
the third is − 76.
:
2:2
1
22
3:3
2
36
6 876
8 8
14 14,13,12
