Find the lesser of the two consecutive integers with a sum greater than 16

Let n be an integer number, the next integer number is n+1. These numbers n and n+1 are two consecutive integers.

Their sum is n+n+1=2n+1 and is greater than 16, thus

2n+1>16.

Solve this inequality:

2n>16-1,

2n>15,

n>7.5.

Since n is integer, then the smallest integer that sutisfies this inequality is 8 and the next n+1=8+1=9.

the lesser of two consecutive integers is 8.