Question: I need to show that $x \sim y$ if $x=2y$. I started off by assuming that $x,y \in R$. Since $x=2y$, $y=x/2$. Since $y \neq 2x$, $\sim$ is not symmetric. Could I approach the problem is this way?

Answer: 
Yes, you can. Note that all you have to do is to find a pair of real numbers $x,y$ such that $x \sim y$ but $y \nsim x$. Take $x = 2, y = 1$.
Yes, you are correct. The relation is not symmetric.

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