Intermediate Algebra (11th edition)

What occupation in the table on the preceding page is expected to see the greatest

change? The least change?

We want the greatest change,without regard to whether the change is an increase

or a decrease. Look for the number in the table with the greatest absolute value. That

number is for home health aides, since Similarly, the least change is

for word processors and typists: |-11.6|=11.6.

|48.7|=48.7.

8 CHAPTER 1 Review of the Real Number System

NOW TRY
EXERCISE 6
Refer to the table in Example 6
on the preceding page. Of the
security guards, file clerks, and
customer service representa-
tives, which occupation is ex-
pected to see the least change
(without regard to sign)?

NOW TRY

OBJECTIVE 6 Use inequality symbols.The statement

is an equation—a statement that two quantities are equal. The statement

(read “4 is not equal to 6”)

is an inequality—a statement that two quantities are notequal.

If two numbers are not equal, one must be less than the other. When reading from

left to right, the symbol means “is less than.”

and All are true.

Reading from left to right, the symbol means “is greater than.”

and All are true.

In each case, the symbol “points” toward the lesser number.

The number line in FIGURE 8shows the graphs of the numbers 4 and 9. We know

that On the graph, 4 is to the left of 9. The lesser of two numbers is always to

the left of the other on a number line.

46 9.

6

5

127 5, 9 7-2, - 4 7-6, 70

7

06

4

3

86 9, - 66 15, - 6 6-1,

6

4 Z 6

4 + 2 = 6

67

4 < 9

081 2 3 4 5 9

FIGURE 8

NOW TRY
EXERCISE 7
Use a number line to deter-
mine whether each statement
is trueor false.

(a)

(b)

NOW TRY ANSWERS

6. security guards


7. (a)false (b)true

- 7 6- 6

- 5 7- 1

Inequalities on a Number Line

On a number line,

abif ais to the right of b.

Determining Order on a Number Line

Use a number line to compare and 1 and to compare and.

As shown on the number line in FIGURE 9, is located to the left of 1. For this

reason,- 66 1.Also, From 1 7-6. FIGURE 9,- 5 6-2,or - 2 7-5.

- 6

- 6 - 5 - 2

EXAMPLE 7

–6 –5 –4 –3 –2 –1 0 1

FIGURE 9

CAUTION Be careful when ordering negative numbers.Since is to the left

of on the number line in FIGURE 9, or In each case, the

symbol points to -5,the lesser number.

- 2 - 56 - 2, - 2 7- 5.

- 5

NOW TRY