Q. 215.0( 3 Votes )

Solve the followi

Answer :

Given








For this inequation to be true, there are two possible cases.


i. x – 5 > 0 and x – 2 > 0


x – 5 + 5 > 0 + 5 and x – 2 + 2 > 0 + 2


x > 5 and x > 2


x (5, ∞) (2, ∞)


However, (5, ∞) (2, ∞) = (5, ∞)


Hence, x (5, ∞)


ii. x – 5 < 0 and x – 2 < 0


x – 5 + 5 < 0 + 5 and x – 2 + 2 < 0 + 2


x < 5 and x < 2


x (–∞, 5) (–∞, 2)


However, (–∞, 5) (–∞, 2) = (–∞, 2)


Hence, x (–∞, 2)


Thus, the solution of the given inequation is (–∞, 2) (5, ∞).


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