Anyone here know anything about inequalities and ratios?

Just try testing it out and see if it makes sense. For example set X to 4 (four ostriches) and Y to 5 (five emus). Now your equation gives 8 ≤ 5, which is false and implies that having four ostriches and five emus is a bad idea.

Of course, since that configuration is supposed to be fine, you know you have something wrong.

EDIT: After seeing the rest of the posts here, I think the moral here is that you should always test your solutions with a few examples to make sure that you're not including or excluding too much.

that is correct

EDIT: I can't read

ostriches must never be more than twice number of emus -> rephrase to emus must outnumber ostriches at least 2 to 1. Which becomes 2y > x, or x <= 2y

There are two parts to what you mentioned: the equation, and the graph.

As for the equation, you just have to put "The ratio of the number of ostriches (x) to the number of emus (y) must never be more than 2:1 otherwise the ostriches attack the emus" into mathematical form. If the ostriches (x) are two times the number of emus (y) or less, then everything is OK. In other words, x = 2y is OK, and x < 2y is OK. Simplifying, you get x <= 2y.

Now for the graph. You didn't mention whether or not you know how to graph x <= 2y, so I'll just go over it briefly. You should know how to map x = 2y, so do that. Now that you have your line, the "less than" part of the equation includes everything above the line, so shade in that area. Basically, the shaded part tells you that, as x goes up, y includes any number above a certain minimum (1/2 of x).

I hope I explained that clearly enough for you.

[Edit: Sorry for the original typo.]

Testing some simple or extreme cases to figure out if what you wrote makes sense is SOLID ADVICE, so I agree with everybody around here.

To me, the quickest way to think this algebraically is: the ratio ostriches to emus is x/y. Well they say this must be LESS (or equal) than 2:1, so x/y <= 2/1. Move things around (they all must be positive, so no complications here), and you get x<=2y, which is the correct answer. Well, to be more precise, 0<=x<=2y, since the problem does not allow for ostriches made from anti-matter, I think.

For the graph, as Khalaq said, always start with the equality x=2y, that is, y=x/2 (a line which is "flatter" than y=x). Now, careful NOT to follow blind rules (some people think that "<" is always "below", or always "to the left" which just does not work at all). I like two ways of reasoning this:

i) THE "THINK" WAY: move one of your variables and THINK. From the line, would MORE ostriches be a problem? Well, yes, they would kill the emus! "More ostriches" means "more x", which is "to the right". Since RIGHT=BAD, the correct graph is to the LEFT of the line.
(You could try instead MORE emus, or LESS ostriches, whatever, pick one and THINK.)

ii) THE "TRICK" WAY: I know the region I want is one of the two sides of the line.... Well, pick a point in one of the regions and test it! Usually I try (x,y)=(0,0), but in this particular case I am unlucky and my favorite point is just ON the line... So I try, say, (x,y)=(10,1) which happens to be below the line (check the graph), and it is a BAD point (emu viscera everywhere, or note that "10<(2)(1)" is FALSE!), so the correct region must be ABOVE the line.

Cheers!

I'd like to thank everyone but I'd gone to bed before any of the responses. We should be going over it in class tomorrow.
Thanks again everyone!