Solving for a Specified Variable

Solve the following formula for c.

Multiply by the LCD, abc.

Distributive property

Simplify.

Subtract acto get both terms

with con the same side.

Factor out c.

c= Divide by b-a.

ab

b-a

c 1 b-a 2 =ab

bc-ac=ab

bc=ac+ab

abca

1

a

b =abca

1

b

b +abca

1

c

b

abca

1

a

b =abca

1

b

+

1

c

b

1

a

=

1

b

+

1

c

EXAMPLE 9

462 CHAPTER 7 Rational Expressions and Applications

Goal: Isolate c, the

specified variable.

Pay careful

attention

here.

NOW TRY
EXERCISE 9
Solve the following formula
for x.

2

w

=

1

x

• 
  

3

y

NOW TRY ANSWER
9.x= 2 ywy+ 3 w

CAUTION Students often have trouble in the step that involves factoring out the

variable for which they are solving. In Example 9,we needed to get both terms with

con the same side of the equation. This allowed us to factor out con the left, and then

isolate it by dividing each side by

When solving an equation for a specified variable, be sure that the specified

variable appears alone on only one side of the equals symbol in the final equation.

b-a.

NOW TRY

Complete solution available
on the Video Resources on DVD

Identify each of the following as an expressionor an equation.Then simplify the expression or

solve the equation. See Example 1.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   5. 
      
      
      
      6. 
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   8. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   

10.Explain why the equation in Exercise 9is easy to check.

When solving an equation with variables in denominators, we must determine the values that

cause these denominators to equal 0 , so that we can reject these extraneous values if they

appear as potential solutions. Find all values for which at least one denominator is equal to 0.

Write answers using the symbol. Do not solve. See Examples 3–7.

11. 
    
    
    
    12. 
        
    
    
    
    


12. 
    
    
    
    14. 
        
    
    
    
    

8

1 x- 721 x+ 32

=

7

3 x- 10

• 
  

  1
  1 x+ 321 x- 42

  
  

1

2 x+ 1

7

x

+

9

x- 4

= 5

3

x+ 2

• 
  

5

x

= 1

Z

3

4

x-

1

2

x= 0

2

3

x-

9

4

x=- 19

3

5

x-

7

10

x= 1

2

3

x-

9

4

x

3

5

x-

7

10

x

4

7

x+

4

5

x= 1

7

8

x+

1

5

x= 1

4

7

x+

4

5

x

7

8

x+

1

5

x

7.6 EXERCISES

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