Basic Mathematics for College Students

700 Chapter 8 Summary and Review

SECTION 8.3 Solving Equations Using Properties of Equality

An equationis a statement indicating that two

expressions are equal. All equations contain

an equal symbol. The equal symbol

separates an equation into two parts: the left

side and the right side.



DEFINITIONS AND CONCEPTS EXAMPLES

Equations:

3

2

t 6 t

1

3

2 x 4  10 5(a4) 11 a

A number that makes an equation a true

statement when substituted for the variable is

called a solutionof the equation.

Determine whether 2 is a solution of.

Check:

Substitute 2 for each.

True

Since the resulting statement, 66, is true, 2 is a solution ofx 4  3 x.

6  6

2  4 3( 2 ) x

x 4  3 x

x 4  3 x

Equivalent equationshave the same solutions. and are equivalent equations because they have the

same solution, 8.

x 2  6 x 8

To solve an equationisolate the variable on

one side of the equation by undoing the

operations performed on it using properties of

equality.

Addition (Subtraction) property of equality:If

the same number is added to (or subtracted

from) both sides of an equation, the result is

an equivalent equation.

Solve: Solve:

x 12 c 7

x 5  5  7  5 c  9  9  16  9

x 5  7 c 9  16

Multiplication (Division) property of equality:

If both sides of an equation are multiplied (or

divided) by the same nonzero number, the

result is an equivalent equation.

Solve:

m 6

3 a

m

3

b3( 2 )

m

3

 2 Solve:

y 5

10 y

10



50

10

10 y 50

Use a check to determine whether the given number is a

solution of the equation.

Fill in the blanks.

43. An is a statement indicating that two
    expressions are equal.

1,

2

y 1



12

y 1

3, 5b 2  3 b 8  5

30, 2, a^2 a 1  0

x

5

 6

84, x 34  50 3, 5y 2  12

44. To solve means to find all the values of
    the variable that make the equation a
    statement.
    Solve each equation. Check the result.


45. 
    
    
    
    46. 
        
    
    
    
    


46. 
    
    
    
    48. 
        
    
    
    
    


47. 
    
    
    
    50. 
        
    
    
    
    


48. 
    
    
    
    52. 
        
    
    
    
    


49. 54.^15
    16

6 b (^0) s 3
3 
q
2.6
4
3
t 12
t
1
2

3
2
120  5 c
a3.716.9 100  7 r
x 9  12 y 32
x 8  10
REVIEW EXERCISES