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Example 3 Solve - 6x > 24  x Î N
Solution :
- 6x > 24
1 (- 6x) > 1 (24) ...(Multiplying by 1/6 to both sides)
6 6
Þ - x > 4
Þ x < - 4 ....(inequality reverses due to change
of sign on both the sides)
Þx = - 5, - 6, -7 .....so on.  x Î N
Example 4 Solve the inequality 2 (x + 1) - 3 (x - 4/3) > 7x  x Î Q
Solution :
2(x + 1) - 3 (x - 4/3) > 7x  x Î Q
2x + 2 - 3x + 4 > 7x
- x + 6 > 7x
- x + 6 + x > 7x + x ......(adding x on both sides)
Example 5 Solve 
Solution :
For any x, x2 ³ 0 \ x2 + 5 > 0
(Multiplying by x2 + 5 to both the sides)
(x2 + 5)  £ (x2 + 5) 
x - 3 £ 2 ..... (a < b and c > 0 then ac < bc)
Þ x - 3 + 3 £ 2 + 3
Þ x £ 5
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