Find all the numbers such that as a third of a number increased by half that number is at least 3 less than the same number

Let the number be n. n - (n/3+n/2) ≥3. So n-5n/6≥3, n/6≥3, n≥18.

Let’s test the solution. A third of 18 is 6; increase by half of 18 and we get 15, which is 3 less than 18.

Now try a number bigger than 18, say 24. A third is 8; increase by 12 and we get 20, which is 4 less than 24, and 4 is bigger than 3 so 20 is at least 3 less than 24. Note that if we put n=12, we don’t satisfy the inequality, because the difference is only 2.