No Identity Element For $x, y ∈$ $\mathbb{R}$, let $x△y = 2(x + y)$. Then $△$ is a binary operation on $\mathbb{R}$.
Show that there is no identity element for $△$ on $\mathbb{R}$.
I have tried $x△e = e△x=x$
I don't know what else to do.

The operator is easily seen to be commutative, so we can just solve
$$x\triangle e=2(x+e)=x\implies e=-x/2$$
But the identity cannot depend on $x$, so there is no identity in the first place.
