Introduction to Inequalities

Definition

An inequality is a mathematical statement which shows that two values are not equal.

a ≠ b means that a is not equal to b. It means that either a is less or greater than b.

There are special symbols that show how things are not equal.

a < b means that a is less than b

a > b means that a is greater than b

a ≤ b means that a is less than or equal to b

a ≥ b means that a is greater than or equal to b

To compare two numbers, we use the symbols, <, > or =.

Example

Use <, >, or = to compare the numbers given below

18

21

72

38

109

163

Solution

Step 1:

Since 18 is less than 21 we write 18 < 21

Step 2:

As 72 is greater than 38, we write 72 > 38

Step 3:

As 109 is less than 163, we write 109 < 163

Problem 1

Use <, >, or = to compare the numbers given below

15

23

67

41

127

199

336

153

Solution

Step 1:

Since 15 is less than 23 we write 15 < 23

Step 2:

As 67 is greater than 41, we write 67 > 41

Step 3:

As 127 is less than 199, we write 127 < 199

Step 4:

As 336 is greater than 153, we write 336 > 153

Problem 2

Use <, >, or = to compare the numbers given below

29

18

78

97

172

146

331

463

Solution

Step 1:

Since 29 is greater than 18, we write 29 > 18

Step 2:

As 78 is less than 97, we write 78 < 97

Step 3:

As 172 is greater than 146, we write 172 > 146

Step 4:

As 331 is less than 463, we write 331 > 463