Solution Manual For Intermediate Algebra For College Students, 6th Edition

Name: Solution Manual For Intermediate Algebra For College Students, 6th Edition
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Chapter 1
Algebra, Mathematical Models, and Problem Solving
1.1 Check Points
1. a.

eight times a number five more
8 5 8 5x x  

b.

the quotient of a decreased bynumber and seven twice the number
2 2
7 7
x x
x x  

2.
replace with 10
23 0.12
23 0.12(10)
23 1.2
21.8
x
x
 
 


At age 10, the average neurotic level is 21.8.
3.
replace with 13
2
2
2
8 6( 3)
8 6(13 3)
8 6(10)
8 6(100)
8 600
608
x
x 
  
 
 
 


4. a. 2010 is 3 years after 2007.
replace with 3
2
2
2.7 5.6 8
2.7(3) 5.6(3) 8
2.7(9) 5.6(3) 8
24.3 16.8 8
49.1
x
S x x
S
  
  
  
  


b. The model value, 49.1, is the same as the actual
data value shown in the figure.
5. a. true; Because the number 13 is an element of the
set of integers.
b. true; Because 6 is not an element of {7, 8, 9, 10},
the statement is true.
6. a. 8 is less than 2; true
b. 7 is greater than 3; true
c. 1 is less than or equal to 4; false
d. 5 is greater than or equal to 5; true
e. 2 is greater than or equal to 14; true
7. a.  2 5x x  
b.  1 3.5x x 
c.  1x x  
1.1 Concept and Vocabulary Check
1. variable
2. expression
3. bth to the nth power; base; exponent
4. formula; modeling; models
5. natural
6. whole
7. integers
8. rational
9. irrational
10. rational; irrational
11. left
12. 2; 5; 2; 5
13. greater than
14. less than or equal to
1

Chapter 1: Algebra, Mathematical Models, and Problem Solving
2
1.1 Exercise Set
2. 6x 
4. 9x 
6. 2x
8. 5 4x 
10. 1
3 2 x
12. 5 3
x 
14. 6
10 x
16.  8 6 5 8 30 38   
18.  8 3 4 24 4 20   
20.    
21 1 1 1
2 2 4 4
2 1 1   
22.  2
8 7 8 4 64 56 4 8 4 12       
24.    
 
3 3
6 5 8 6 6 5 2
6 5 8
6 40 46
   
 
  
26.    2
8 4 8 3 64 4 5 64 20 44      
28. {1, 2, 3}
30. {–6, –5, –4, –3}
32. {10, 11, 12, . . .}
34. {1, 3, 5, 7}
36. true; Nine is an integer.
38. true; Nine is a rational number.
40. false; Nine is not an irrational number.
42. true; Five is not an irrational number.
44. false; 1
4 is a rational number.
46. true;
 is not a rational number.
48. false;
 is a real number.
50. –7 is less than –3; true
52. 3 is greater than –8; true
54. 0 is less than –5; false. 0 is greater than –5.
56. –5 is less than or equal to 1; true
58. –3 is less than or equal to –7; false. –3 is greater
than –7.
60. –3 is less than or equal to –3; true
62. –3 is greater than or equal to –3; true
64. 4 is less than or equal to 1
2
 ; false. 4 is greater
than 1
2
 .
66.  2 4x x  
68.  4 3x x  
70.  2 5x x  
72.  3x x 
74.  5x x  
76.  2x x 
78.  3.5x x 
80. true

Intermediate Algebra for College Students 6E Section 1.2
82. false;    4 1, 2,3, 4,5 .
84. true
86. false; The value of {x | x is an integer between 4
and 0} = { 3, 2, 1}   , not { 4, 3, 2, 1, 0}    .
88. false; Three times the sum of a number and five is
represented by  3 5x  , not 3 5x  .
90. 4.6 0.02
4.6 0.02(30)
4.0
R x 
 

The average resistance to happiness at age 30 is 4.0.
92. [4.6 0.02(20)] [4.6 0.02(70)]
4.2 3.2
1.0
  
 

The difference between the average resistance to
happiness at age 20 and at age 70 is 0.4.
94. 2
2
4.6 5.5 5
4.6(3) 5.5(3) 5
62.9
63
G x x  
  


According to the formula, 63 new college programs
in green studies were created in 2008. The formula
underestimated the actual value by 3 programs.
96. 5 5 5
( 32) (86 32) (54) 30
9 9 9
C F     
30C is equivalent to 86F.
98. 2
2
4 60 16
4 60(3) 16(3)
4 180 16(9)
4 180 144
184 144 40
h t t  
  
  
  
  
Three seconds after it was kicked, the ball’s height
was 40 feet.
100. – 116. Answers will vary.
118. does not make sense; Explanations will vary.
Sample explanation: Though this value is beyond
the capabilities of a calculator, it still exists. This
particular expression can be obtained via several
software applications.
120. does not make sense; Explanations will vary.
Sample explanation: The model can be used to
estimate the number in 2000 by letting 0.x 
122. false; Changes to make the statement true will vary.
A sample change is: Some integers are not whole
numbers.
124. true
126.  2 3 3 5 45   
128. 26 is not a perfect square and 26 cannot be
simplified. Consider the numbers closest to 26,
both smaller and larger, which are perfect squares.
The first perfect square smaller than 26 is 25. The
first perfect square larger than 26 is 36. We know
that the square root of 26 will lie between these
numbers. We have 36 26 25.     If we
simplify, we have 6 26 5.     Therefore,
26 lies between –6 and –5.
129. –5 and 5 are both a distance of five units from zero
on a real number line.
130.
4
16 3(2) 16 3(16) 16 48 64 8
12 (10 6) 12 (4) 8 8
  
   
  
131. 2(3 5)
2(3(4) 5)
2(12 5)
2(17)
34
x 
 
 


6 10
6(4) 10
24 10
34
x 
 
 

1.2 Check Points
1. a. 6 6  because 6 is 6 units from 0.
b. 4.5 4.5 because 4.5 is 4.5 units from 0.
c. 0 0 because 0 is 0 units from 0.
2. a. 10 ( 18) 28    
3

Chapter 1: Algebra, Mathematical Models, and Problem Solving
4
b. 0.2 0.9 0.7  
c. 3 1 6 5 1
5 2 10 10 10
      
3. a. If 8,x   then ( 8) 8.x    
b. If 1
3 ,x  then 1
3 .x  
4. a. 7 10 7 ( 10) 3     
b. 4.3 ( 6.2) 4.3 6.2 10.5    
c. 4 1 4 1 3
5 5 5 5 5
 
        
 
5. a. 2
( 5) ( 5)( 5) 25    
b. 2
5 (5 5) 25     
c. 3
( 4) ( 4)( 4)( 4) 64      
d.
4
3 3 3 3 3 81
5 5 5 5 5 625
        
              
        
6. a. 32 8
4  

b. 2 5 2 4 8
3 4 3 5 15
   
          
   
7. 2 2
3 5 12 2( 4)
3 25 12 2(16)
3 25 6(16)
3 25 96
22 96
74
   
   
  
  
  

8.
3
4 3( 2)
2 (6 9)
4 3( 8)
2 ( 3)
4 24
2 3
20
5
4
 
 
 
  

 


 
9. Commutative Property of Addition: 4 9 9 4x x  
Commutative Property of Multiplication:
4 9 4 9x x   
10. a. 6 (12 ) (6 12) 18x x x      
b. 7(4 ) ( 7 4) 28x x x     
11. 4(7 2) 28 8x x    
12. 2 2
2 2
2
2
3 14 11
(14 ) (3 11 )
(14 1) (3 11)
15 14
x x x x
x x x x
x x
x x
  
   
   
 
13. 8(2 5) 4
16 40 4
16 4 40
12 40
x x
x x
x x
x
 
  
  
 
14. 6 4[7 ( 2)]
6 4[7 2]
6 4[9 ]
6 36 4
42 4
x
x
x
x
x
  
   
  
  
 
1.2 Concept and Vocabulary Check
1. negative number
2. 0
3. positive number
4. positive number
5. positive number
6. negative number
7. positive number
8. divide
9. subtract
10. absolute value; 0; a
11. a; a
12. 0; inverse; 0; identity

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Intermediate Algebra for College Students 6E Section 1.3
4. a. The drug concentration is increasing from 0 to 3
hours.
b. The drug concentration is decreasing from 3 to
13 hours.
c. The drug’s maximum concentration is 0.05
milligram per 100 milliliters, which occurs after
3 hours.
d. None of the drug is left in the body.
5. The minimum x-value is –100, the maximum x-
value is 100, and the distance between consecutive
tick marks is 50. The minimum y-value is –100, the
maximum y-value is 100, and the distance between
consecutive tick marks is 10.
1.3 Concept and Vocabulary Check
1. x-axis
2. y-axis
3. origin
4. quadrants; four
5. x-coordinate; y-coordinate
6. solution; satisfies
1.3 Exercise Set
2. – 10.
12. x  ,x y
3  3, 0
2  2, 5 
1  1, 8 
0  0, 9
1  1, 8
2  2, 5
3  3, 0
14. x  ,x y
3  3, 1 
2  2, 0
1  1,1
0  0, 2
1  1,3
2  2, 4
3  3,5
9

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Chapter 1: Algebra, Mathematical Models, and Problem Solving
10
16. x  ,x y
3  3, 10 
2  2, 8 
1  1, 6 
0  0, 4
1  1, 2
2  2, 0
3  3, 2
18. x  ,x y
3 7
3, 2
 
 
 
2  2,3
1 5
1, 2
 
 
 
0  0, 2
1 3
1, 2
 
 
 
2  2,1
3 1
3, 2
 
 
 
20. x  ,x y
3  3, 2
2  2,1
1  1, 0
0  0, 1
1  1, 0
2  2,1
3  3, 2
22. x  ,x y
3  3, 6 
2  2, 4 
1  1, 2 
0 

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Intermediate Algebra for College Students 6E Section 1.3
24. ( , )
9
3 ( 3, )
2
2 ( 2, 2)
1
1 ( 1, )
2
0 (0, 0)
1
1 (1, )
2
2 (2, 2)
9
3 (3, )
2
x x y
  
  
  



26. x  ,x y
3  3, 28 
2  2, 9 
1  1, 2 
0  0, 1
1  1, 0
2  2, 7
3  3, 26
28. [–10, 10, 2] by [– 4, 4, 2]
This matches graph d.
30. [–40, 40, 20] by [–1000, 1000, 100]
This matches graph a.
32. The equation that corresponds to 1Y in the table is
(b), 2
1y x . We can tell because all of the points
( 3,9) , ( 2, 4) , ( 1,1) , (0, 0) , (1,1) , (2, 4) , and
(3,9) are on the graph 2
y x , but all are not on
any of the others.
34. Yes. It passes through the point (0, 0) .
36. (0, 2)
38. The values of 1Y and 2Y are the same when
2x   and 1x  .
40. 4 2y x 
42. 2 2y x 
11

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