Intermediate Algebra (11th edition)

OBJECTIVE 5 Use absolute value.Geometrically, the absolute valueof a

number a, written is the distance on the number line from 0 to a. For example, the

absolute value of 5 is the same as the absolute value of because each number lies

five units from 0. See FIGURE 7on the next page.

- 5

|a|,

In the expression the symbol “ ” is being used in two ways. The first

indicates the additive inverse (or opposite) of and the second indicates a negative

number, Since the additive inverse of is 5, it follows that

- 1 - 52 = 5.

- 5. - 5

- 5,

- 1 - 52 , - -

6 CHAPTER 1 Review of the Real Number System

NOW TRY
EXERCISE 4
Decide whether each state-
ment is trueor false. If it is
false, tell why.

(a)All integers are irrational
numbers.

(b)Every whole number is an
integer.

Determining Relationships Between Sets of Numbers

Decide whether each statement is trueor false.

(a)All irrational numbers are real numbers.

This is true. As shown in FIGURE 5, the set of real numbers includes all irrational

numbers.

(b)Every rational number is an integer.

This statement is false. Although some rational numbers are integers, other

rational numbers, such as and^23 -^14 ,are not. NOW TRY

EXAMPLE 4

OBJECTIVE 4 Find additive inverses.Look at

FIGURE 6. For each positive number, there is a negative

number on the opposite side of 0 that lies the same

distance from 0. These pairs of numbers are called

additive inverses, opposites, or negatives of each

other. For example, 3 and - 3 are additive inverses.

–3 –2 –1 0 1 2 3

Additive inverses (opposites)

FIGURE 6

Uses of the Symbol

The symbol “ ” is used to indicate any of the following:

1. a negative number,such as or

2. the additive inverse of a number,as in “ is the additive inverse of 4”;

3. subtraction,as in 12 - 3.

- 4

- 9 - 15;

-



Additive Inverse

For any real number a, the number -ais the additive inverseof a.

For any real number a,  1 a 2 a.

 1 a 2

We change the sign of a number to find its additive inverse. As we shall see later,

the sum of a number and its additive inverse is always 0.

Numbers written with positive or negative signs, such as and

are called signed numbers.A positive number can be called a signed number even

though the positive sign is usually left off. The table in the margin shows the additive

inverses of several signed numbers.

+4,+8,-9, -5,

NOW TRY ANSWERS

4. (a)false; All integers are
   rational numbers.
   (b)true

Number Additive Inverse

6

4

8.7

00

• 8.7

(^23) - (^23)

• 4
  
  
  • 6
  
  
  
  

The number 0 is its own additive
inverse.