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.

$$(x+2)>3$$