Find all pairs of consecutive odd positive integers

Asked by admin @ in Math viewed by 307 People

Question 23 Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

Class X1 - Maths -Linear Inequalities Page 122

Answered by admin @


Let 2x+1 and 2x +3 are two positive odd integers .
a/C to question ,
2x +1 < 10
=> 2x < 10-1 = 9
=> 2x < 9
x < 9/2

and 2x + 3 < 10
=> 2x < 7
x < 7/2

and sum of (2x+1) and (2x +3) >11
2x +1 + 2x +3 > 11
4x +4 > 11
4x > 7
x > 7/4

now, plotting all these values on number line . (see attachment)
a/C to attachment ,
7/4 < x < 7/2
hence, possible value of x = 2, 3
when x = 2 then, (2×2+1,2×2+3)= (5, 7)
when x = 3 then, (2×3+1,2×3+3) = (7,9)

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