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After graphing y = |x| + x, express this equation as a piece-wise function with no absolute values.

I did graph it; it was simple (following is a sketch without values):

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Now the final answer included } y = 0, where x<and=0, and y = 2x, where x>0. I found the equations by looking/calculating the slope for each separate piece. However, what I do not understand is why is it x>0 INSTEAD of x>AND=0 for y = 2x. This is perhaps trivial and easy, but I don't comprehend the reason.

Thanks for your patience.