Beginning Algebra, 11th Edition

The symbol means “is greater than.”

8 is greater than 2.

To keep the meanings of the symbols and clear, remember that the symbol

always points to the lesser number.

Lesser number Lesser number

The symbol means “is less than or equal to.”

5 is less than or equal to 9.

If either the part or the part is true, then the inequality is true.The state-

ment is true, since is true.

The symbol means “is greater than or equal to.”

9 is greater than or equal to 5.

Using Inequality Symbols

Determine whether each statement is trueor false.

(a) This statement is false because

(b) The statement is true, since.

(c) The statement is true, since

(d) Both and are false, so is false.

(e) Since this statement is true.

(f ) Since this statement is false.

(g)

Get a common denominator.

Both statements and are false. Therefore, is false.

NOW TRY

OBJECTIVE 5 Translate word statements to symbols.

Translating from Words to Symbols

Write each word statement in symbols.

EXAMPLE 5

6

15 Ú

2 3

6

15 =

10 15

6

157

10 15

6

15

Ú

10

15

6

15

Ú

2

3

96 9 9 = 9,

12 Ú 12 12 =12,

25 Ú 30 25730 25 = 30 25 Ú 30

15 ... 20 # 2 15 ... 20 # 2 15640.

5 + 36 19 5 + 3619 8619

6 Z 5 + 1 6 = 5 + 1.

EXAMPLE 4

9 Ú 5

Ú

5 ... 9 569

< ◊

5 ... 9

...

1578

8615

< >

872

7

18 CHAPTER 1 The Real Number System

NOW TRY
EXERCISE 4
Determine whether each
statement is trueor false.

(a)

(b)

(c)

(d)

5

9

7

11

7 ... 7

574 # 2

12 Z 10 - 2

NOW TRY ANSWERS

(a)true (b)false
(c)true (d)false

(a) (b)
(c) 11 ... 20

10 Z 8 - 2 50715

NOW TRY
EXERCISE 5
Write each word statement in
symbols.

(a)Ten is not equal to eight
minus two.

(b)Fifty is greater than fifteen.

(c)Eleven is less than or equal
to twenty.

(a)Twelve equalsten plustwo.

12 = 10 + 2

(b)Nine is less thanten.

9610

(c) Fifteen is not equal toeighteen.

15 Z 18

(d)Seven is greater thanfour.

77 4

(e) Thirteen is less than or equal to

forty.

13 ... 40

(f )Eleven is greater than or equal to

eleven.