n, n + 2 - two consecutive even integers
the sum of two consecutive even integers is greater than or equal to 34
n + (n + 2) ≥ 34
n + n + 2 ≥ 34
2n + 2 ≥ 34 subtract 2 from both sides
2n ≥ 32 divide both sides by 2
n ≥ 16
Answer: The smallest possible integers is equal 16.