Poster Project, I am a Mathematician, Algebra, Even Plus Odd

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Hopefully, the first thing you did was try a few examples:

2 + 3 = 5
4 + 7 = 11
22 + 23 = 45

Of course, this doesn't prove anything. (Notice, though, that to disprove the statement it would be enough to find one counterexample. If you can find one odd number and one even number whose sum is even, that suffices to disprove the statement. But I could give five billion examples of even and odds whose sum was odd, and that wouldn't prove anything -- there could always be one example which I haven't considered ... and that may be the one which doesn't work.)

We can't prove this statement by considering specific numbers. Instead, we have to find an abstract way of describing evens and odds.

You've probably seen the magical mathematical x, which acts as a placeholder for an unknown number. You can think of x as the name of this placeholder. There is no particular reason to use x -- other than tradition, of course. In fact, any letter will do. One important thing to remember though, is that once I've used x once in a problem, then, in that problem, x always has to refer to the same thing.

In the problem at hand, we need to be sure x is even (or odd).

What makes a number even?

Is any old x divisible by 2? What can we do to make sure that it is?