Ex 5.1, 23 - Chapter 6 Class 11 Linear Inequalities (Important Question)

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Ex 5.1, 23 Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11. Let the smaller odd positive integer be x Since the larger integer is consecutive odd, Given, Both integers are smaller than 10, i.e. x < 10 & Since x < 10 & x < 8 x < 8 Sum of the two integers is more than 11. ∴ x + (x + 2) >A 11 2x + 2 > 11 2x > 11 – 2 2x > 9 x > 9/2 x > 4.5 Hence, x > 4.5 & x < 8 Integers greater than 4.5 but less than 8 are 5, 6, 7 Odd integers are 5, 7 Hence x = 5 or x = 7 Thus, different sets of positive integers possible are (5, 7), (7, 9)