Proof by contradiction for irrational numbers

I am supposed to prove "If n is irrational then n+(1/2) is irrational" by contradiction. so far I have "assume n+(1/2) is rational, therefore it can be written as a/b where a and b are integers and b =/= 0" but I don't know how that would contradict or really where to go from there. Any help at all would be much appreciated :)

n+(1/2) = a/b then
n = (a/b) - (1/2) = (2a - 1)/(2b)
You got n = (2a - 1)/(2b) this a contradiction because you may write n like a rational number (2a-1)/(2b)