When one divides 2x by 2, why isn't the x part divided by 2 as well?

I was thinking that maybe it's because 2x is one term only but it can also be written as x+x and I think that if one were to divide x+x by 2, one would have to divide both x's. So clearly in 2x, one must divide the x's. I looked at the math later and realized that this makes 1x. Okay so then what makes 2x a single term and its equivalent, x+x, two terms?

Thanks for feedback.