finding cdf of standard uniform

A question about unifrom rv.

If $\displaystyle X \;and\; Y$ are independent $\displaystyle standard \;uniform$ random variables. and we want to find the cumulative distribution of $\displaystyle X-2Y$

to find the cdf here, can I suppose that $\displaystyle W=X-2Y,0<w<1$ and then find $\displaystyle P(W \leq w)$

so, I have $\displaystyle P(W \leq w) = P(X-2Y \leq W) = P(Y \geq \frac{W-X}{2}) = 1 - P(Y < \frac{W-X}{2}) $

and integrate $\displaystyle 1 - \displaystyle \int _0^w\;\int_0^{\frac{w-x}{2}}\;dy\;dx$

is this right or am I wrong?