Page 134 - Basic College Mathematics with Early Integers

S E C T I O N 2.1 I INTRODUCTION TO VARIABLES AND ALGEBRAIC EXPRESSIONS 111

If you are having difficulty replacing variables with numbers, first replace each
variable with a set of parentheses, then insert the replacement number within the
parentheses.
Using this method in Example 4, we have:
2
2
x + z - 3 = 1 2 + 1 2 - 3
2
= 152 + 142 - 3
= 25 + 4 - 3
= 26

Concept Check What’s wrong with the solution to the following problem?
Evaluate 3x + 2y for x = 2 and y = 3.
Solution: 3x + 2y = 3132 + 2122
= 9 + 4
= 13

51F - 322
Example 5 The expression can be used to write degrees Fahrenheit PRACTICE 5
9
F as degrees Celsius C. Find the value of this expression for Evaluate 51F - 322 for
F = 86. 9
F = 41.
51F - 322 5186 - 322
Solution: =
9 9
51542
=
9
270
=
9
= 30

Thus 86°F is the same temperature as 30°C.
Work Practice 5

Objective Translating Phrases into Variable Expressions

To aid us in solving problems later, we practice translating verbal phrases into alge-
braic expressions. Recall from Section 1.8 that certain key words and phrases sug-
gest addition, subtraction, multiplication, or division.These are reviewed next.

Addition Subtraction Multiplication Division
( ) ( ) () # ( )

sum difference product quotient
Answer
plus minus times divide 5. 5
added to subtract multiply shared equally among
Concept Check Answer
more than less than multiply by per The replacement values were switched.
If done correctly, we have:
increased by decreased by of divided by
3x + 2y = 3122 + 2132
= 6 + 6
total less double/triple divided into
= 12