Answer to a bigggggggg problem

It is kind of like two wrongs make a right.  Let us say that x and

y are both positive.  Then the meaning of -(x) + (y) is just y - x and (y) - -

(x) = y + x, subtracting a negative number is the same as adding the positive

number.  Now, let us say n is a positive integer. Then n * x can be thought of

as adding x to itself n times which explains why a positive number times a

negative number is always negative.  So, what does -(n) * x?  Well,

multiplication is commutative,  i.e., x * y = y * x.  So -(n) * x = x * -(n)

or  -(n) * x  = (-1 * n ) * x = ( n * -1 ) * x = n * ( -1 * x )  because

multiplication is also associative = n * -(x).  All of which is to say that -n

* x is the same as adding -x to itself n times. Therefore, -n * -x is the same

as adding -(-x) to itself n times.  And, I think we all agree that -(-x)

better be +x.  Hope this is not too confusing!