Beginning Algebra, 11th Edition

69. true 71. 73.


70. 77.Five is less than seventeen; true 79.Five is
    not equal to eight; true 81.Seven is greater than or equal to fourteen;
    false 83.Fifteen is less than or equal to 15; true 85.


71. 
    
    
    
    89. 
        
        
        
        91. 
            
            
            
            93. 
                
            
            
            
            
        
        
        
        
    
    
    
    


72. 
    
    
    
    97. (a) (b)9.5 (c)8.075;
        walking (5 mph) 99.Answers will vary.
    
    
    
    

Section 1.3 (pages 26–27)

1.B 3.A 5. while

7.The exponent 2 applies only to its base, which is x. 9. (a) 11

(b) 13 11. (a) 16 (b) 24 13. (a) 64 (b) 144 15. (a)

(b) 17. (a) (b) 19. (a) 52 (b) 114 21. (a)25.836

(b)38.754 23. (a) 24 (b) 28 25. (a) 12 (b) 33 27. (a) 6

(b) 29. (a) (b) 31. (a) (b) 33. (a) 12 (b) 55

35. (a) 1 (b) 37. (a)3.684 (b)8.841 39. 41.


36. 
    
    
    
    45. 
        
        
        
        47. 
            
            
            
            49. 
                
                
                
                51. 53.An
                    expression cannot be solved—it indicates a series of operations to per-
                    form. An expression is simplified. An equation is solved. 55.yes
                    57.no 59.yes 61.yes 63.yes 65.no 67.
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


37. 
    
    
    
    71. 
        
        
        
        73. 75.expression 77.equation 79.equation 81.64.9 yr 83.73.8 yr
            85.Life expectancy has increased over 13 yr during this time.
        
        
        
        
    
    
    
    

Section 1.4 (pages 34–36)

1.2,866,000 3. 5. 7.82.60 9. 4 11. 0

13.One example is There are others. 15.true 17.true

19.false

In Exercises 21–25, answers will vary.

21. 
    
    
    
    23. 
        
        
        
        25. 
            
            
            
            27. (a)3, 7
                (b)0, 3, 7 (c) (d) 0, 3, 5.9, 7
                (e) (f )All are real numbers. 29.
            
            
            
            
        
        
        
        
    
    
    
    


22. 
    
    
    
    33. 
        
        
        
        35. (a)A
        
        
        
        
    
    
    
    

(b)A (c)B (d)B 37. (a) 7 (b) 7 39. (a) (b) 8

41. (a) (b) 43. 6 45. 47. 49. 3 51.This is not
    true. The absolute value of 0 is 0, and 0 is not positive. A more accurate
    way of describing absolute value is to say that absolute value is never
    negative, or absolute value is always nonnegative. 53. 55.


42. 4 59. , or 3.5 61. , or 63. , or 2
    65.true 67.true 69.true 71.false 73.true 75.false
    77.fuel and other utilities, 2004 to 2005 79.apparel and upkeep,
    2006 to 2007

|-3.5| -|- 6 | - 6 | 5 - 3 |

• 11 - 7

(^3434) - 12 - (^23)

• 8


•  7 ,  5


• 9, 0, 3, 7 - 9 ,- 114 ,- 53 , 0.1,

(^12) , (^58) , 1 34 - 3 12 , - (^23) , (^37)  5 , p , - 3
 13.

• 52,000 -11.2; 8.6

16 - 43 x=13; 4 2 x+ 1 =5; 2 3 x= 2 x+8; 8

x+ 8 =18; 10

x- 4 7 - x x- (^818) x 61 x- 42
(^281712) x x+ 9
16
27
2
7
13
6
4
3
9
5
13
12
7
8
7
3
5
3

2 x^3 = 2 #x#x#x , 2 x# 2 x# 2 x= 12 x 23.

1.3...2.5 14.7- 40 #0.13

975 - 4 16 Z 19 21 ...^242075

15 = 5 + 10

18 + 222 = 100

3 Ú 3 ; 3 # 16 + 42 # 2 = 60 10 - 17 - 32 = 6

A-1

In this section we provide the answers that we think most students will ob-
tain when they work the exercises using the methods explained in the text.
If your answer does not look exactly like the one given here, it is not nec-
essarily wrong. In many cases, there are equivalent forms of the answer
that are correct. For example, if the answer section shows and your an-
swer is 0.75, you have obtained the right answer, but written it in a differ-
ent (yet equivalent) form. Unless the directions specify otherwise, 0.75 is
just as valid an answer as
In general, if your answer does not agree with the one given in the
text, see whether it can be transformed into the other form. If it can, then it
is the correct answer. If you still have doubts, talk with your instructor. You
might also want to obtain a copy of the Student’s Solutions Manualthat
goes with this book. Your college bookstore either has this manual or can
order it for you.

3

4.

3

4

Answers to Selected Exercises

THE REAL NUMBER SYSTEM

Section 1.1 (pages 10–13)

1.true 3.false; This is an improper fraction. Its value is 1. 5.false;
The fraction is written in lowest terms as 7.false; Productrefers
to multiplication, so the product of 10 and 2 is 20. 9.prime
11.composite; 13.composite;
15.neither 17.composite; 19.prime 21.composite;
23.composite; 25.composite;

27. 
    
    
    
    29. 
        
        
        
        31. 
            
            
            
            33. 
                
                
                
                35. 37.C 39.
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


28. 
    
    
    
    43. 
        
        
        
        45. or 47. 9 49. or 51. or
        
        
        
        
    
    
    
    


29. or 55. 12 57. 59. 10 61. 18 63. or


30. or 67.A 69. 71. 73. 75. or 77.

or 79. or 81. 83. 85. 87. 89. or

91. 93.6 cups 95. in. 97. in. 99. ft 101. in.
    103.8 cakes (There will be some sugar left over.) 105. yd


92. in. 109. 111.about million, or 5,320,000


93. (a) (b) (c) (d)

Section 1.2 (pages 19–21)

1.false; means that 6 is used as a factor 2 times; so
3.false; 1 raised to anypower is 1. Here,
5.false; , which simplifies to ,
or 22. The common error leading to 42 is adding 4 to 3 and then multiply-
ing by 6. One must follow the order of operations. 7. 9 9. 49

11. 144 13. 64 15. 1000 17. 81 19. 1024 21. 23.
    25.0.064 27. 32 29. 58 31.22.2 33. or 35. 12


12. 13 39. 26 41. 4 43. 42 45. 5 47. 41 49. 95 51. 90


13. 14 55. 9 57. true 59. false 61.
    true 63. 45 Ú 46 ;false 65. 66772 ;false 67. 2 Ú 3 ;false

16 ... 16 ; 61 ... 60 ; 0 Ú 0 ;

(^4930) , (^1 1930)
16
81
1
36

4 + 318 - 22 means 4+ 3 # 6 4 + 18

13 = 1 # 1 # 1 =1.

62 62 = 6 # 6 =36.

1

6

1

3

1

4

1

2

3 38 201 5 258

(^16 58)
1211 1 81 169 618 43 5 245
5 38 10120 , 5 201 59 23 41 3617 2067 , 3 207
43
1 8 ,
5
24
29
24 ,
8
9
2
3
11
(^115)
37
47
84
47 ,
(^103) , 3 31 161 2435 , 1 2411
85 256 56 ,^1 516512 ,^5 125385 ,^7 53
24
35
6
5
1
5
16
25
5
6
1
2 # 7 # 13 # (^192)

2 # 2 # 31 2 # 2 # 5 # 5 # 5

3 # 19

2 # 3 # 5 2 # 2 # 2 # 2 # 2 # 2

1

3.

13

39

1

–6 –4 –2 0 2

–6 –4 –2 0 2 4 –4 –2 0 2 4

–3^45 –1^5814212