Inequalities are used to compare any two statements.
Inequality: An inequality is a mathematical statement in which two real numbers or two expressions are connected by <,>, ≤ or ≥.
Example:
(i) 2x – 3 ≤ 6
(ii) x – 4 ≥ 5
Operations on inequalities:
i) The same number can be added to (or subtracted from) the given inequality with out changing its sign.
Example – 1: x+5 < 6
Subtracting 5 from both sides, we get x<1.
Example – 2: x-5 < 6
Adding 5 on both sides, we get x<11.
ii) Both the sides of the inequality can be multiplied (or divided) by the same positive number with out changing its sign.
Example-1: x<5
Multiplying both sides by 2, we get 2x<10.
Example-2: 5x<20
Dividing both sides by 5, we get x<4.
iii) Both the sides of the inequality can be multiplied (or divided) by the same negative number by changing its sign.
Example-1: -x<3
Multiplying both sides by -1, we get x>-3
Example-2: -5x<20
Dividing both sides by -5, we get x>-4.
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