Intermediate Algebra (11th edition)

SECTION 2.5 Linear Inequalities in One Variable 99

Complete solution available
on the Video Resources on DVD

2.5 EXERCISES

Concept Check Match each inequality in Column I with the correct graph or interval in

Column II.

III

1. A.

2. B.

3. C.

4. D.

5. E.

6. F.

7.Concept Check A student solved the following inequality as shown.

Solution set:

WHAT WENT WRONG?Give the correct solution set.

8.Concept Check Dr. Paul Donohue writes a syndicated column in which readers ques-

tion him on a variety of health topics. Reader C. J. wrote, “Many people say they can

weigh more because they have a large frame. How is frame size determined?” Here is Dr.

Donohue’s response:

“For a man, a wrist circumference between 6.75and 7.25in. [inclusive] indicates a

medium frame. Anything above is a large frame and anything below, a small frame.”

Using xto represent wrist circumference in inches, write an inequality or a three-part

inequality that represents wrist circumference for a male with the following.

(a)a small frame (b)a medium frame (c)a large frame

(Source: The Gazette.)

Solve each inequality. Give the solution set in both interval and graph form. See Examples 1–5.

9. 
   
   
   
   10. 
       
       
       
       11. 
           
       
       
       
       
   
   
   
   


10. 
    
    
    
    13. 
        
        
        
        14. 
            
        
        
        
        
    
    
    
    


11. 
    
    
    
    16. 
        
        
        
        17. 
            
        
        
        
        
    
    
    
    


12. 
    
    
    
    19. 
        
        
        
        20. 
            
        
        
        
        
    
    
    
    


13. 
    
    
    
    22. 
        
        
        
        23. 
            
        
        
        
        
    
    
    
    

24. 25. 26.

27. 28.

29. 30.

31. 32.

33. 34.

7

5

110 x- 126

2

3

16 x+ 52

2

3

13 x- 12 Ú

3

2

12 x- 32

• 31 x- 6272 x- 2 - 21 x+ 42 ... 6 x+ 16


• 14 +r 2 + 2 - 3 r6- 14 - 19 +x 2 - 5 + 4 xÚ 4

x- 21 x- 42 ... 3 x x- 31 x+ 12 ... 4 x

6 x- 4 Ú- 2 x 2 x- 8 Ú- 2 x

3 x- 2

• 5

66

2 x- 5

• 4

75

3 x- 1

4

75

5 x- 6

8

68

• 2.5x...-1.25 5 x+ 2 ...- 48 4 x+ 1 ...- 31
  
  
  • -1.3xÚ-5.2
  
  
  
  

2

3

• x... 12

3

4

xÚ 30

5 x+ 6676 4 x6- 16 2 x7- 10

x- 4 Ú 12 x- 3 Ú 7 3 k+ 1722

1 - q, - 164

x...- 16

4 x

4

...

- 64

4

4 xÚ- 64

• 36 x 63 3 - 3, 3 4


• 3 ...x... 3 1 - 3, 3 2

xÚ 3 1 - q, 3 4

x 63 1 3, q 2

x 73

x... 3

0 3

0 3