Think about it like this. 0+x would equal x+0 but if you did the opposite then the answer would still equal x+0 because 'x' is an indefinite number and if you times, divide, subtract or plus then it would still equal x+0 or x-0 or x*0 or x divide 0.
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zero pair
They equal zero.
Zero can be expressed as the sum of any two opposite mixed number.
If the opposite is meant to be the additive opposite and not the multiplicative opposite, then their sum is zero. The reason is that is what defines an additive opposite!
If by "opposite" you mean "additive inverse", the sum is zero. For example, 5 + (-5) = 0.