Proving A is Open: Union of Open Balls

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Homework Statement

Let (X,d) be a metric space and let A be a non-empty subset of X. Prove that A is open if and only if it can be written as the union of a family of open balls of the form Br(x) = {y ∈ X|d(x,y) < r} (the radius r may depend on the point x).

Homework Equations

The Attempt at a Solution

I have no idea where to start with this.

 

[Dick]

What's the definition of an open set in a metric space? Is the union of open sets open? If you look these things up, it will help you a lot.