How to solve a integer part inequality?

I was thinking to just do $x+2 >3$ and then it will give me $x>1$ so I add the difference between 3 and 2 only to the right part ,because not adding it will give me $x in (1,+infinite)$ so if I plug in 1.99 it will give me 3 which is not good because 3 > 3 is false.

$(x+2)>3$