Posted by **olivia** on Tuesday, December 20, 2011 at 6:45pm.

prove -x-y=-y-x, for all integers

- math -
**MathMate**, Wednesday, December 21, 2011 at 9:28am
I do not know what grade you're in, but questions of this sort could go quite deep into algebra.

Since x,y are integers, which belong to a ring in which additions are commutative, so if we write the subtractions as inverses of addition, the above would be invoking commutativity in the ring-addition:

-x-y

=(-x)+(-y) inverse of addition

=(-y)+(-x) commutativity of addition

=-y-x inverse of addition

For high-school algebra, then it would be the commutative property of addition and subtraction.

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