Intermediate Algebra (11th edition)

54 CHAPTER 2 Linear Equations, Inequalities, and Applications

Complete solution available
on the Video Resources on DVD

2.1 EXERCISES

1.Concept Check Which equations are linear equations in x?

A. B. C. D.

2.Which of the equations in Exercise 1are nonlinear equations in x? Explain why.

3.Decide whether 6 is a solution of by substituting 6 for x. If it is not a

solution, explain why.

4.Use substitution to decide whether is a solution of

If it is not a solution, explain why.

Decide whether each of the following is an expressionor anequation.See Example 1.

Solve each equation, and check your solution. If applicable, tell whether the equation is an

identity or a contradiction. See Examples 2, 3, and 6.

11. 
    
    
    
    12. 
        
        
        
        13. 
            
        
        
        
        
    
    
    
    


12. 
    
    
    
    15. 
        
        
        
        16. 
            
        
        
        
        
    
    
    
    


13. 
    
    
    
    18. 
        
    
    
    
    


14. 
    
    
    
    20. 
        
    
    
    
    


15. 
    
    
    
    22. 
        
    
    
    
    


16. 
    
    
    
    24. 
        
    
    
    
    


17. 
    
    
    
    26. 
        
    
    
    
    


18. 
    
    
    
    28. 
        
    
    
    
    


19. 
    
    
    
    30. 
        
    
    
    
    


20. 
    
    
    
    32. 
        
    
    
    
    


21. 
    
    
    
    34. 
        
    
    
    
    


22. 
    
    
    
    36. 
        
    
    
    
    


23. 
    
    
    
    38. 
        
    
    
    
    


24. 
    


25. 
    


26. 
    


27. 
    


28. 
    


29. 
    

    45.Concept Check To solve the linear equation

    
    

,

we multiply each side by the least common denominator of all the fractions in the equation.

What is this least common denominator?

8 x

3

-

5 x

4

=- 13

23 - 1 x- 12 + 44 = 5 + 3 - 16 x- 72 + 9 x 4

• 33 x- 12 x+ 524 =- 4 - 3312 x- 42 - 3 x 4

436 - 11 + 2 x 24 + 10 x= 2110 - 3 x 2 + 8 x

732 - 13 + 4 x 24 - 2 x=- 9 + 211 - 15 x 2

41 x+ 22 - 8 x- 5 =- 3 x+ 9 - 21 x+ 62

• 3 x+ 6 - 51 x- 12 =- 5 x- 12 x- 42 + 5


• 32 x- 15 x+ 224 = 2 + 12 x+ 72 - 36 x- 14 x+ 824 = 9 + 16 x+ 32

23 x- 12 x+ 42 + 34 = 21 x+ 12 432 x- 13 - x 2 + 54 =- 12 + 7 x 2

• 21 x+ 32 - x- 4 =- 31 x+ 42 + 2 412 x+ 72 = 2 x+ 25 + 312 x+ 12

6 x- 413 - 2 x 2 = 51 x- 42 - 10 - 2 x- 314 - 2 x 2 = 21 x- 32 + 2

2 x+ 31 x- 42 = 21 x- 32 6 x- 315 x+ 22 = 411 - x 2

312 x+ 12 - 21 x- 22 = 5 41 x- 22 + 21 x+ 32 = 6

21 x+ 32 =- 41 x+ 12 41 x- 92 = 81 x+ 32

• 2 x+ 5 x- 9 = 31 x- 42 - 5 - 6 x+ 2 x- 11 =- 212 x- 32 + 4


• 51 x+ 12 + 3 x+ 2 = 6 x+ 4 51 x+ 32 + 4 x- 5 = 4 - 2 x

312 t- 42 = 20 - 2 t 213 - 2 x 2 =x- 4

12 w+ 15 w- 9 + 5 =- 3 w+ 5 - 9 - 4 x+ 5 x- 8 + 4 = 6 x- 4

9 x+ 1 = 7 x- 9 7 x- 5 x+ 15 =x+ 8 2 x+ 4 - x= 4 x- 5

7 x+ 8 = 1 5 x- 4 = 21 5 x+ 2 = 3 x- 6

• 10 x+ 12 - 4 x=- 3 - 10 x+ 12 - 4 x+ 3 = 0

41 x+ 32 - 21 x+ 12 - 10 41 x+ 32 - 21 x+ 12 + 10

• 3 x+ 2 - 4 =x - 3 x+ 2 - 4 - x= 4
  
  
  • 2 51 x+ 42 - 31 x+ 62 = 91 x+ 12.
  
  
  
  

31 x+ 42 = 5 x

1

2

x-

1

x

3 x+x- 1 = 0 8 =x^26 x+ 2 = 9 = 0