Page 618 - Basic College Mathematics with Early Integers

8.5 EQUATIONS AND PROBLEM SOLVING Objectives

Write Phrases as Algebraic
Expressions.
Objective Writing Phrases as Algebraic Expressions
Write Sentences as Equations.
Now that we have practiced solving equations for a variable, we can extend consid-
erably our problem-solving skills. We begin by reviewing how we write phrases as Use Problem-Solving Steps
algebraic expressions using the following key words and phrases as a guide: to Solve Problems.

Addition Subtraction Multiplication Division Equal Sign

sum difference product quotient equals
plus minus times divided by gives
added to subtracted from multiply into is/was
more than less than twice per yields
increased by decreased by of amounts to
total less double is equal to

Example 1 Write each phrase as an algebraic expression. Use x to represent PRACTICE 1
“a number.” Write each phrase as an
a. 7 increased by a number b. 15 decreased by a number algebraic expression. Use x to
c. the product of 2 and a number d. the quotient of a number and 5 represent “a number.”
e. 2 subtracted from a number f. the sum of 9 and twice a number a. twice a number
b. 8 increased by a number
Solution:
c. 10 minus a number
a. In words:
increased d. 10 subtracted from a number
7 a number
by e. the quotient of 6 and a
number
T T T
Translate: 7 + x f. the sum of 14 and triple a
b. In words: number
decreased
15 a number
by
T T T
Translate: 15 - x
c. In words:
the product
of
ƒ
2 and a number
T T T
Translate: 2 # x or 2x
d. In words:
the quotient
of
ƒ
a number and 5

T T T x
Translate: x , 5 or
5
e. In words: subtracted
2 a number Answers
from
1. a. 2x b. 8 + x c. 10 - x
T 6
Translate: x Î - Î 2 Continued on next page d. x - 10 e. 6 , x or x f. 14 + 3x
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