Beginning Algebra, 11th Edition

104 CHAPTER 2 Linear Equations and Inequalities in One Variable

OBJECTIVE 4 Write expressions for two related unknown quantities.

NOW TRY

EXERCISE 11

Two numbers have a sum of

18. If one of the numbers is
    represented by m, find an ex-
    pression for the other number.

NOW TRY ANSWER

11. 18 - m

Translating a Phrase into an Algebraic Expression

Perform each translation.

(a)Two numbers have a sum of 23. If one of the numbers is represented by x, find

an expression for the other number.

First, suppose that the sum of two numbers is 23, and one of the numbers is 10.

How would you find the other number? You would subtract 10 from 23.

This gives 13 as the other number.

Instead of using 10 as one of the numbers, use x. The other number would be obtained

in the same way—by subtracting xfrom 23.

To check, find the sum of the two numbers:

as required.

(b)Two numbers have a product of 24. If one of the numbers is represented by x, find

an expression for the other number.

Suppose that one of the numbers is 4. To find the other number, we would divide

24 by 4.

In the same way, if xis one of the numbers, then we divide 24 by xto find the other

number.

The other number NOW TRY

24

x

24

4

x+ 123 - x 2 =23,

23 - x.

23 - 10

EXAMPLE 11

This gives 6 as the other number.

The product 6 # 4 is 24.

x- 23 is notcorrect.

Complete solution available
on the Video Resources on DVD

2.3 EXERCISES

Using the methods of this section, what should we do first when solving each equation? Do

not actually solve.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   5. 6.0.9x+0.3 1 x+ 122 = 6
   
   
   
   

2

3

x-

1

6

=

3

2

x+ 1

3

4

z=- 15

7 x+ 8 = 1 7 x- 5 x+ 15 = 8 +x 3 12 t- 42 = 20 - 2 t

7.Concept Check Which equation does nothave {all real numbers} as its solution set?

A. B. C. D.

8.Concept Check The expression is equivalent to which of the

following?

A. B. C. D.

Solve each equation, and check your solution. See Examples 1–5, 9, and 10.

9. 
   
   
   
   10. 
       
       
       
       11. 12.- 7 w- 4 = 10 13. 4 p- 5 = 2 p 14. 6 q- 2 = 3 q
       
       
       
       
   
   
   
   

3 x+ 2 = 14 4 x+ 3 = 27 - 5 z- 4 = 21

0.03x-0.3 3 x- 3 3 x- 10 3 x- 30

1003 0.03 1 x- 1024

3 x= 2 x

1

2

5 x= 4 x+x 21 x+ 62 = 2 x+ 12 x=0.5x

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