Beginning Algebra, 11th Edition

Evaluating Expressions

Find the value of each algebraic expression for x= 5.

EXAMPLE 1

1.3 Variables, Expressions, and Equations

NOW TRY
EXERCISE 1
Find the value of each alge-
braic expression for

(a) 9 k (b) 4 k^2

k=6.

NOW TRY ANSWERS

1. (a) 54 (b) 144


2. (a) 40 (b) 2 (c) 15

(a) 8 x

Let

= 40 Multiply.

= 8 # 5 x=5.

= 8 #x

(b)

Let

Square 5.

= 75 Multiply.

= 3 # 25

= 3 # 52 x=5.

= 3 #x^2

3 x^2

52 = 5 # 5

NOW TRY

CAUTION In Example 1(b), means , not Unless parenthe-

ses are used, the exponent refers only to the variable or number just before it.Use

parentheses to write 3 x# 3 xwith exponents as 13 x 22.

3 x^23 #x^23 x# 3 x.

Evaluating Expressions

Find the value of each expression for and

(a)

Let and

Multiply.

= 31 Add.

= 10 + 21

= 2 # 5 + 7 # 3 x= 5 y=3.

2 x+ 7 y

x= 5 y=3.

EXAMPLE 2

Follow the

rules for order of

operations.

We could use parentheses and write 2152 + 7132.

(b)

Let and

Multiply.

Subtract, and then divide.

(c)

Let and

Apply the exponents.

Multiply.

= 7 Subtract.

= 25 - 18

= 25 - 2 # 9

= 52 - 2 # 32 x= 5 y=3.

x^2 - 2 y^2

=

21

7

, or 3

=

45 - 24

10 - 3

= x= 5 y=3.

9 # 5 - 8 # 3

2 # 5 - 3

9 x- 8 y

2 x-y

NOW TRY
EXERCISE 2
Find the value of each expres-
sion for and

(a) (b)

(c) 4 x^2 - y^2

6 x- 2 y

2 y- 9

3 x+ 4 y

x= 4 y=7.

32 = 3 # 3

52 = 5 # 5

NOW TRY

OBJECTIVE 2 Translate word phrases to algebraic expressions.

Using Variables to Write Word Phrases as Algebraic Expressions

Write each word phrase as an algebraic expression, using xas the variable.

(a)The sumof a number and 9

or “Sum” is the answer to an addition problem.

(b) 7 minusa number

“Minus” indicates subtraction.

x 7 is incorrect. We cannot subtract in either order and get the same result.

7 - x

x+ 9, 9 +x

EXAMPLE 3