Intermediate Algebra (11th edition)

OBJECTIVE 2 Write equations from given information. The symbol for

equality, is often indicated by the word is.

Translating Words into Equations

Translate each verbal sentence into an equation.

EXAMPLE 1

=,

68 CHAPTER 2 Linear Equations, Inequalities, and Applications

CAUTION Because subtraction and division are not commutative operations,

it is important to correctly translate expressions involving them.For example,

“2 less than a number” is translated as not

“A number subtracted from 10” is expressed as not

For division, the number by whichwe are dividing is the denominator, and the number

into whichwe are dividing is the numerator.

“A number divided by 13” and “13 divided into x” both translate as

“The quotient of xand y” is translated as

x

y^.

x

13.

10 - x, x- 10.

x- 2, 2 - x.

NOW TRY
EXERCISE 1
Translate each verbal sen-
tence into an equation, using
xas the variable.

(a)The quotient of a number
and 10 is twice the
number.

(b)The product of a number
and 5, decreased by 7, is
zero.

NOW TRY ANSWERS

1. (a) 10 x = 2 x (b) 5 x- 7 = 0

NOW TRY

OBJECTIVE 3 Distinguish between simplifying expressions and solving

equations.An expression translates as a phrase. An equation includes the sym-

bol, with expressions on both sides, and translates as a sentence.

Distinguishing between Simplifying Expressions

and Solving Equations

Decide whether each is an expressionor an equation.Simplify any expressions, and

solve any equations.

(a)

There is no equals symbol, so this is an expression.

Distributive property

Simplified expression

(b)

Because there is an equals symbol with expressions on both sides, this is an

equation.

6 + 2 x- 4 x+ 7 =- 1 Distributive property

213 +x 2 - 4 x+ 7 =- 1

213 +x 2 - 4 x+ 7 = - 1

=- 2 x+ 13

= 6 + 2 x- 4 x+ 7

213 +x 2 - 4 x+ 7

213 +x 2 - 4 x+ 7

EXAMPLE 2

=

Any words that

indicate the idea of

“sameness” translate

as=.

Verbal Sentence Equation

Twice a number, decreased by3, is42.

The product of a number and 12,

decreased by 7, is105.

The quotient of a number and the

number plus 4is28.

The quotient of a number and 4,

plus the number, is10.

x

4

+x= 10

x

x+ 4

= 28

12 x- 7 = 105

2 x- 3 = 42