Prove that for every integer x, is even.This is what i have so far:

Prove by contradiction,

Suppose is ODD

(where k is any integer)

now plug in (2k + 1) for is ODD

= ODD

= ODD

= ODD

This is False!, ex. when k = 1, is EVEN

Therefore is EVEN

Does this all seem correct? i am very new to proofs. any criticism is appreciated

Thank you