Basic Mathematics for College Students

Chapter 8 Summary and Review 701

SECTION 8.4 More About Solving Equations

A strategy for solving equations:

1. Simplifyeach side. Use the distributive
   property and combine like terms when
   necessary.


2. Isolate the variable term.Use the addition
   and subtraction properties of equality.


3. Isolate the variable.Use the multiplication
   and division properties of equality.


4. Checkthe result in the original equation.

DEFINITIONS AND CONCEPTS EXAMPLES

Solve: 6 x+ 2 = 14

To isolate the variable, we use the order of operations rule in reverse.

• To isolate the variable term, 6x, we subtract 2 from both sides to
  undo the addition of 2.


• To isolate the variable,x, we divide both sides by 6 to undo the
  multiplication by 6.

 2  2  14  2 Subtract 2 from both sides to isolate 6x.

6  12 Do the subtractions.

Divide both sides by 6 to isolate x.

x 2

The solution is 2. Check by substituting it into the original equation.

6 x

6



12

6

x

6 x

When solving equations, we should simplify

the expressions that make up the left and right

sides before applying any properties of

equality.

Solve:

Distribute the multiplication by 2.

Combine like terms:.

To eliminate on the right, add

to both sides.

Combine like terms.

To isolate the variable term ,

subtract 4 from both sides.

7 Simplify each side of the equation.

To isolate , divide both sides by 7.

The solution is 1. Check by substituting it into the original equation.

y 1

y

7 y

7



7

7

y 7

7 y 4  4  11  4 7 y

7 y 4  11

6 y 4 y 11 yy y y

6 y 4  11 y 2 y 4 y 6 y

2 y 4  4 y 11 y

2(y2) 4 y 11 y

Solve each equation. Check the result.

55. 
    
    
    
    56. 
        
    
    
    
    


56. 
    
    
    
    58. 
        
    
    
    
    


57. 12 a 9  4 a 15 60. 8 t3.2 4 t1.6

3

4

c 10  11

n

5

 2  4

5 x 4  14 98.6t129.2

61.

62.

63.

64. 8(1.5r0.5)3.28

2(m40) 6 m3(4m80)

2(x5)5( 3 x4) 3

5(2x4) 5 x 0

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