Intermediate Algebra (11th edition)

The following table summarizes results about positive and negative numbers in

both words and symbols.

SECTION 1.1 Basic Concepts 9

Words Symbols

Every negative number is less than 0. If ais negative, then

Every positive number is greater than 0. If ais positive, then

0 is neither positive nor negative.

a 7 0.

a 6 0.

Symbol Meaning Example

is not equal to

is less than

is greater than

is less than or equal to

Ú is greater than or equal to - 8 Ú- 10

... 6 ... 6

7 37 - 2

6 - 46 - 1

Z 3 Z 7

NOW TRY
EXERCISE 8
Simplify. Then tell whether
the resulting statement is true
or false.

• |- 12 |Ú 2 # 5

Inequality Symbols

In addition to the symbols Z, 6 ,and 7 ,the symbols ... and Úare often used.

Using Inequality Symbols

The table shows some examples of uses of inequalities and why they are true.

EXAMPLE 8

Inequality Why It Is True

6 # 4 ... 5152 24 625

• 3 Ú- 3 - 3 =- 3


• 9 Ú- 12 - 9 7- 12


• 2 ...- 2 - 2 =- 2

6 ... 8 668

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

–2 is not included.

The interval (–2, ∞)

FIGURE 10

Notice the reason that is true. With the symbol if either the

part or the part is true, then the inequality is true. This is also the case with the

symbol.

In the last row of the table, recall that the dot in indicates the product

6 4,or 24, and 5152 means 5 5 ,or 25. Thus, the inequality 6 # 4 ... 5152 be-

6 # 4

»



- 2 ...- 2 ◊, <

The set of numbers greater than is an example of an intervalon the number

line. To write intervals, we use interval notation.We write the interval of all num-

bers greater than - 2 as 1 - 2, q 2.

- 2

NOW TRY ANSWER

8. 
   
   
   
   • 12 Ú 10 ; false
   
   
   
   

comes which is true. NOW TRY

OBJECTIVE 7 Graph sets of real numbers.Inequality symbols and variables

are used to write sets of real numbers. For example, the set

consists of all the real numbers greater than. On a number line, we graph the ele-

ments of this set by drawing an arrow from to the right. We use a parenthesis at

- 2 to indicate that - 2 is notan element of the given set. See FIGURE 10.

- 2

- 2

5 x|x7- 26

24 ... 25,