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, x^{2} ³ 0 \ x^{2} + 5 > 0
(Multiplying by x^{2} + 5 to both the sides)
(x^{2} + 5) £ (x^{2} + 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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