Given that $n$ is an integer and $0 < 4n <30$, what is the sum of all possible integer values of $n$?
I want to find all the integers $n$ that satisfy the inequality $0 < 4n <30$. To do this, I can divide everything by 4 to get $0 < n < 7.5$. Now I can see that the possible integer values of $n$ are 1, 2, 3, 4, 5, 6, and 7. To find the sum of these values, I can add them up: 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. 