Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is - Maths - Linear Inequalities

Question

Find all pairs of consecutive even positive integers, both
of which are larger than 5 such that their sum is less than
23

Gopal Mohanty · Accepted Answer

Let x be the smaller of the two consecutive even positive integers Then, the other integer is x + 2 Since both the integers are larger than 5, x > 5 (1) Also, the sum of the two integers is less than 23 x + (x + 2) < 23 ⇒ 2x + 2 < 23 ⇒ 2x < 23 – 2 ⇒ 2x < 21

From (1) and (2), we obtain 5 < x < 10 5 Since x is an even number, x can take the values, 6, 8, and 10 Thus, the required possible pairs are (6, 8), (8, 10), and (10, 12)

Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.