By the triangle inequality
2n +15 + 3n > n + 30
5n + 15 > n + 30
4n < 15
n < 15/4
n < 3.75
And
n + 30 + 2n + 15 > 3n
3n + 45 > 3n
True for all positive n
And
3n + n + 30 > 2n + 15
3n + 30 > 2n + 15
n > -15
Assuming that we want positive integer answers.....
n = ( 1, 2 , 3)
DON'T HELP! THIS IS AN ACTIVE AoPS HOMEWORK PROBLEM! I realize that problems may be challenging. Ask on the message board and we will be glad to help you!