Prove using proof by contradiction: if x is an even integer, then 3x + 7 is odd

Suppose 3x + 7 is even when x is even

then 3x + 7 = 2m where m is some integer

3x = 2m - 7

which means that 3x is odd because 2m - 7 must be odd

but x is even and 3x is even so our original assumption is wrong

So 3x - 7 must be odd when x is even.