Basic Mathematics for College Students

666 Chapter 8 An Introduction to Algebra

Fill in the blanks.

1. An , such as , is a statement
   indicating that two expressions are equal.


2. Any number that makes an equation true when
   substituted for the variable is said to the
   equation. Such numbers are called.


3. To an equation means to find all values of the
   variable that make the equation true.


4. To solve an equation, we the variable on one
   side of the equal symbol.


5. Equations with the same solutions are called
   equations.


6. To the solution of an equation, we substitute
   the value for the variable in the original equation and
   determine whether the result is a true statement.


7. Consider.
   a. What is the left side of the equation?
   b. Is this equation true or false?
   c. Is 5 the solution?
   d. Does 6 satisfy the equation?


8. For each equation, determine what operation is
   performed on the variable. Then explain how to undo
   that operation to isolate the variable.
   a.
   b.
   c.
   d.


9. Complete the following properties of equality.
   a. If , then
   and
   b. If , then and


10. a. To solve , do we multiply both sides of the
    equation by 10 or 20?
    b. To solve , do we subtract 4 from
    both sides of the equation or divide both
    sides by 4?


11. Simplify each expression.
    a. b.

c. d. 6 

h

6

5 t

5

x 7  7 y 2  2

4 k 16

10 h 20

(c0)

a

c



b

ab ca b

acb acb

ab

8 x 24

x

8

 24

x 8  24

x 8  24

x 6  12

CONCEPTS

(^) x 1  7
VOCABULARY 12. a. To solve , we can multiply both sides by the
reciprocal of. What is the reciprocal of?
b. What is?
Complete each solution to solve the equation.

13. Check:

True

is the solution.

14. Check:

True

is the solution.

15. a. What does the symbol mean?
    b. If you solve an equation and obtain , can
    you write?


16. Fill in the blank:

Check to determine whether the given number is a solution of

the equation.See Example 1.

17. 
    
    
    
    18. 
        
    
    
    
    


18. 
    
    
    
    20. 
        
    
    
    
    


19. 
    
    
    
    22. 
        
    
    
    
    


20. 
    
    
    
    24. 
        
    
    
    
    


21. 
    
    
    
    26. 
        
    
    
    
    


22. 
    
    
    
    28. 
        
    
    
    
    


23. 
    
    
    
    30. 
        
    
    
    
    


24. 
    
    
    
    32. 
        
    
    
    
    


25. 
    
    
    
    34. 
        
    
    
    
    


26. 3, (x4)(x3) 0 36.5, (2x1)(x5) 0

7

3

,  4 a

5

3

3

4

, x

1

8



5

8

4,

2 t

t 2



4

t 2

1,  1

2

a  1

 5 

12

a  1

3, x^2 x 6  0 2, y^2  5 y 3  0

12, 3x 2  4 x 5 5, 5y 8  3 y 2

2, 0 c 80  10 45, 030 r 0  15

8,

x

4

6, 33  98  100

x

2

 30

5, 0.5x2.9 3.5, 1.2x4.7

8, 2b 3  15 2, 5t 4  16

6, x 12  28 110, x 50  60

GUIDED PRACTICE

x x

x 50

50 x



x  40

8( ) 40

8 x



40

8 x 40 8 x 40

x  45

x 5   45   5 45

x 5  45 x 5  45

NOTATION

^541 ^452

^45 ^45

^45 x 8

SECTION 8.3 STUDY SET