Prove "If x and y are irrational numbers, then 3x+4xy+2y is irrational"

Question

How would I go proving this? I tried contrapositive and contradiction approaches but both don't look very correct for proof. For contrapositive I must always assume x to be irrational to reach conclusion but this seems incorrect approach. I appreciate any help you may give. I assume negation of original implication, then I solved for y. This is when I say x = $\sqrt{2}$ an irrational number. The rest is logical, but this assumption of x seems incorrect for proof.

Answer 1

It's false. Let $x=\sqrt{2}/3$ and $y=-\sqrt{2}/2$. Both are irrational but $3x+4xy+2y=-4/3$ is rational.