Basic Mathematics for College Students

4. When we write the expression 9xxas 10x, we say
   we have like terms.


5. On the left side of the equation 4x 9 25, the
   variable xis multiplied by , and then is added to
   that product.


6. On the right side of the equation 16  5 t1, the
   variable tis multiplied by , and then is
   subtracted from that product.
   Fill in the blanks.


7. To solve , we first undo the of
   5 by adding 5 to both sides. Then we undo the
   by 3 by dividing both sides by 3.


8. To solve , we can undo the of 3 by
   subtracting 3 from both sides. Then we can undo the
   by 2 by multiplying both sides by 2.


9. a. Combine like terms on the left side of
   .
   b. Distribute and then combine like terms on the
   right side of.


10. Distribute on both sides of the equation shown
    below.Do not solve.


11. Use a check to determine whether is a solution of
    the equation.
    a. b.


12. a. Simplify:
    b. Solve:
    c. Evaluate for.
    d. Check: Is a solution of?

Complete the solution.

13. Solve:

Check:

is the solution.

14. Fill in the blank:y y

Solve each equation and check the result.See Example 1.

15. 
    
    
    
    16. 
        
    
    
    
    


16. 
    
    
    
    18. 
        
    
    
    
    


17.  33  5 t 2 20. 55  3 w 5

5 q 2  23 3 x 5  13

2 x 5  17 4 p 3  43

GUIDED PRACTICE

 21

 7  21

2( ) 7 21

2 x 7  21

x 14

2 x



28

2 x 28

2 x 7   21 

2 x 7  21

NOTATION

 1 3 x 5 x 9

3 x 5 x x 9

3 x 5  9

3 x 5 x

6 x 5  7 8(x3) 8

 2

7(3x2)4(x3)

 20 4(3x4) 9 x

6 x 8  8 x 24

x 2  3  5

3 x 5  1

CONCEPTS

21. 
    
    
    
    22. 
        
    
    
    
    


22. 
    
    
    
    24. 
        
    
    
    
    

Solve each equation and check the result.See Example 2.

25. 12  7 a 9 26. 15  8 b 1


26. 
    
    
    
    28. 
        
    
    
    
    

Solve each equation and check the result.See Example 3.

29. 
    
    
    
    30. 
        
    
    
    
    


30. 
    
    
    
    32. 
        
    
    
    
    


31. 
    
    
    
    34. 
        
    
    
    
    

Solve each equation and check the result.See Example 4.

35. 
    
    
    
    36. 
        
    
    
    
    


36. 
    
    
    
    38. Solve each equation and check the result.See Example 5.
    
    
    
    


37. 
    


38. 
    


39. 
    


40. 
    


41. 
    


42. 
    


43. 
    


44. 
    


45. 
    


46. 
    


47. 
    


48. 
    

Solve each equation and check the result.See Example 6.

51. 
    
    
    
    52. 
        
    
    
    
    


52. 
    
    
    
    54. 
        
    
    
    
    


53. 
    
    
    
    56. 
        
    
    
    
    


54. 
    
    
    
    58. Solve each equation and check the result.See Example 7.
    
    
    
    


55. 
    


56. 
    


57. 
    


58. 
    

Solve each equation. Check the result.

63.

64.

65. 4(d5)  20  5  2 d

 6 t 7 t 5 t 1  12  3

3 x 8  4 x 7 x 2  8

TRY IT YOURSELF

2 (4x7) 3 2(x2)

2 3(x5)4(x1)

9(T1) 18 T6(T2)

3(A2) 4 A2(A7)

8 y 2  4 y 16 7  3 w 4  9 w

60 r 50  15 r 5 100 ƒ 75  50 ƒ 75

8 y 44  4 y 9 y 36  6 y

5 x 4 x 7 3 x 2 x 2

6 x5(3x1) 58

(19 3 s)(8s1) 35

16 y8(3y2) 24

6 a3(3a4) 30

3.288(1.5y0.5)

10.084(0.5x2.5)

(6t) 12

(4m) 10

20 b2(6b1) 34

9(x11)5(13x) 0

2( 3 a2)a 2

3(2y2)y 5

 6 y 2  1 h 9

1.71.2x 0.64.1x



5

8

 h 25  15

7

16

h 28  21

2

5

c 12  2

5

6

k 5  10

3

5

x 6  12

2

3

t 2  6

 3  3 p 7  1  2 r 8

 5  2 d 0  8  3 c 0

0.7 4 y1.7 0.3 2 x0.9

674 Chapter 8 An Introduction to Algebra