The 2y is throwing me a bit here. To determine if it is reflexive, I have done the following: $x+2x\le 3$, which is a no with counter example (1,2), as that would give me (1,4) and be greater than 3. Is every second number doubled? Ie. (x,2x) or (x,2y)?

I have concluded this relation is not symmetric, as it does not imply $y+2x\le 3$, on the basis that is $x=2\text{}and\text{}y=1$, this would result in $2+2(1)\text{}for\text{}x+2y\text{}but\text{}1+2(2)$ for $y+2x$, which is greater than 3. I have no confidence in this answer however.

I'm floundering on this one. Every time it was touched on during the lecture, it was simple examples, like $x+y$ is even, or if there was an equality, there wasn't a defined set for it.

For determining transitive, what would I use as z?