Properties of Inequations –
(i) Adding the same number or expression to each side of an inequation does not change the inequality. e.r., x – 2 < 4
=> x – 2 + 2 < 4 + 2
=> x < 6
(ii) Subtracting the same number or expression from each side of an inequation does not change the inequality. e,g., x + 3 < 10
=> x + 3 – 3 < 10 – 3
=> x < 7
(iii) Multiplying (or dividing) each side of an inequation by the same positive number does not change
a
the inequality. e,g., ------ < 6
5
a
=> ------- X 5 < 6 X 5
5
=> a < 30
(iv) Multiplying (or dividing) each side of an inequation by the same negative number reverse the inequality. e.g., - x < - 2
=> x > 2 [Multiplying both side by (- 1) ]
And, - 2x < 8
=> x > - 4 [Dividing both side by (- 2)]
Remarks : - (i) a < b ó b > a
(ii) a > b ó b < a
Thus, x > 3 ó 3 < x
And, x < 5 ó 5 > x
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