the answer to that is a mental hospital
In your own words the process of change that the young protagonist suffers from
The sum of number is at least 14 means the sum is either equal to 14 or greater then 14. So,
According to the question,
5x + 2x ≥ 14
= 7x ≥ 14
= x ≥ 14 / 7
= x ≥ 2