Beginning Algebra, 11th Edition

72 CHAPTER 1 The Real Number System

Complete solution available
on the Video Resources on DVD

1.8 EXERCISES

Concept Check In Exercises 1–4, choose the letter of the correct response.

1.Which expression is a simplified form of?

A. B. C. D.

2.Which is an example of a term with numerical coefficient 5?

A. B. C. D. 52 xy^3

x

5

5 x^3 y^7 x^5

• 6 x- 3 - 6 x+ 3 6 x- 3 6 x+ 3
  
  
  • 16 x- 32
  
  
  
  

NOW TRY
EXERCISE 4
Translate the phrase into a
mathematical expression and
simplify.

Twice a number, subtracted

from the sum of the number

and 5

NOTE Examples 2 and 3suggest that like terms may be combined by adding or

subtracting the coefficients of the terms and keeping the same variable factors.

OBJECTIVE 5 Simplify expressions from word phrases.

Translating Words into a Mathematical Expression

Translate the phrase into a mathematical expression and simplify.

The sum of 9, five times a number,

four times the number, and

six times the number

The word “sum” indicates that the terms should be added. Use xfor the number.

simplifies to Combine like terms.

NOW TRY

9 + 5 x+ 4 x+ 6 x 9 + 15 x.

EXAMPLE 4

NOW TRY ANSWERS

3. (a) (b)


4. 1 x+ 52 - 2 x; -x+ 5

9 k- 9 - 125 x+ 6

(e)

Distributive property

Combine like terms.

(f )

Distributive property

Multiply.

Get a common denominator.

=- Combine like terms. NOW TRY

5

6

x+ 4

= -

4

6

x+ 4 -

1

6

x

= -

2

3

x+ 4 -

1

6

x

=-

2

3

x-

2

3

1 - 62 -

1

6

x

-

2

3

1 x- 62 -

1

6

x

=- 2 a- 3

= 10 a- 30 - 12 a+ 27

NOW TRY 512 a- 62 - 314 a- 92

EXERCISE 3
Simplify each expression.

(a)

(b)

1

4

x-

2

3

1 x- 92

5 k- 6 - 13 - 4 k 2

This is an expression to be simplified,

notan equation to be solved.

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