Page 4 - Real Number System_Neat

2
2
| | = | | =
3 3
| | |2| 2
and = =
| | |3| 3

| |
∴ | | =
| |

ii) For = 2 = −3

2
2

| | = | | =
−3 3
| | |2| 2
and = =
| | |−3| 3

| |
∴ | | =
| |

3. Solve the following inequalities

a) − 1 > 2

Solution:

Here
− 1 > 2

⇒ − 1 + 1 > 2 + 1 [Adding 1 to each term]
⇒ > 3

b) − 3 ≤ 5

Solution:
Here,

− 3 ≤ 5
⇒ − 3 + 3 ≤ 5 + 3 [Adding 3 to each term]

⇒ ≤ 8

c) −1 < − 2 < 3

Solution:

Here,