Linear Inequations-20

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Find all pairs of consecutive even positive integers, both of which are larger than 8, such that their sum is less than 25.

Solution: Let x be the smaller of the two consecutive even positive integers. Then, the other even integer is x + 2.

It is given that both the integers are larger than 8 and their sum is less than 25.

Therefore, x > 8 and x + x + 2 < 25

=>x > 8 and 2x + 2 < 25

=> x > 8 and 2x < 23

=> 8 < x < 23/2

=> x = 10 [since, x is an even integer]

Hence, the required pair of even integers is (10, 12)

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