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Now I am trying to show that ##B(r,x)\subseteq S^c##

This should be a simple question, but I am struggling trying to find the right inequlity.

Attempt:

let ##y## be a point in ##B(r,x)##.

I know that ##|x - y| < r##.

I have to somehow show that ##|y| > \rho##

this is where my argument falls apart:

##|y| \leq |y-x| + |x|< r + \rho## (by triangle inequality)

but this doesn't show that ##|y| > \rho##

what am I missing?