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

  • math - ,

    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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