Intermediate Algebra (11th edition)

118 CHAPTER 2 Linear Equations, Inequalities, and Applications

Complete solution available
on the Video Resources on DVD

2.7 EXERCISES

Concept Check Match each absolute value equation or inequality in Column I with the

graph of its solution set in Column II.

IIIIII

1. A.

B.

C.

D.

E.

2. A.

B.

C.

D.

|x|... 9 E.

|x| 69

|x|Ú 9

|x| 79

|x|= 9

|x|Ú 5

|x|... 5

|x| 75

|x| 65

|x|= 5

–5 0 5

–5 0 5

–5 0 5

–5 0 5

–5 0 5

–9 0 9

–9 0 9

–9 0 9

–9 0 9

–9 0 9

3.Concept Check How many solutions will have for each situation?

(a) (b) (c)

4.Explain when to use andand when to use orif you are solving an absolute value equation

or inequality of the form , , or , where kis a

positive number.

Solve each equation. See Example 1.

5. 
   
   
   
   6. 
      
      
      
      7. 
         
      
      
      
      
   
   
   
   


6. 
   
   
   
   9. 
      
      
      
      10. 
          
      
      
      
      
   
   
   
   


7. 
   
   
   
   12. 
       
       
       
       13. 
           
       
       
       
       
   
   
   
   


8. 
   
   
   
   15. 
       
       
       
       16. 
           
       
       
       
       
   
   
   
   

17. 18. 19.

20. 21. 22.

Solve each inequality, and graph the solution set. See Example 2.

23. 
    
    
    
    24. 
        
        
        
        25. 
            
        
        
        
        
    
    
    
    


24. 
    
    
    
    27. 
        
        
        
        28. 
            
        
        
        
        
    
    
    
    


25. 
    
    
    
    30. 
        
        
        
        31. 
            
        
        
        
        
    
    
    
    


26. 
    
    
    
    33. 
        
        
        
        34. 
            
        
        
        
        
    
    
    
    

35.Concept Check The graph of the solution set of | 2 x+ 1 |= 9 is given here.

| 5 - x| 73 |- 5 x+ 3 |Ú 12 |- 2 x- 4 |Ú 5

|x+ 2 | 710 | 4 x+ 1 |Ú 21 | 3 - x| 75

|x|Ú 6 |r+ 5 |Ú 20 | 3 r- 1 |Ú 8

|x| 73 |x| 75 |x|Ú 4

` 2 - |0.02x- 1 |=2.50 |0.04x- 3 |=5.96

5

2

x ` = 14

` 1 +

3

4

` x ` = 7

2

3

` x- 1 ` = 5

1

2

x+ 3 ` = 2

| 5 x- 1 |= 21 | 2 x+ 5 |= 14 | 2 x- 9 |= 18

| 2 x- 1 |= 11 | 2 x+ 3 |= 19 | 4 x- 5 |= 17

| 5 x|= 30 |x- 3 |= 9 |x- 5 |= 13

|x|= 12 |x|= 14 | 4 x|= 20

|ax+b|=k |ax+b| 6 k |ax+b| 7 k

k= 0 k 70 k 60

|ax+b|=k

–5 0 4

Without actually doing the algebraic work, graph the solution set of each inequality,

referring to the graph shown.

(a)| 2 x+ 1 | 69 (b)| 2 x+ 1 | 79