Given two random variables x and y, and a constant c

What conditions are needed to make:

$\displaystyle Prob( w x + y < c ) \approx Prob( w x < c ), \text{ for } w \rightarrow \infty$

Can anyone help?

I think $\displaystyle E(x) < \infty$ and $\displaystyle E(y) < \infty$ might do. Is this right?

tks!!!!