Very easy math
posted by Very easy Math .
my teacher told me that the inverse of addition was subtraction and that the inverse of subtraction was addition...
could you prove it to me
x = (1)x
((1)x)^1
I don't see how I'm suppose to get + x by taking the inverse of x i've always been told in math to just to the opposite of subbtraction which is addition but my teacher is telling me that is a lie and that it's really the inverse of subtraction is addition but I don't see the reasoning behind it
basically can you prove to me that the opposite of subractiion is addition and vise versa??? by taking the inverses????
I don't get it...
like I can prove that the opposite of multiplication is division by taking the inverse and can prove it just by defintion
(5x = 2)5^1 = x = 5^1 (2)
that's how you prove that relationship is really just inverses but what about addition and subtraction how are the inverse relationships...???
Thansk

Use numbers.
6 + 2 = 8
Therefore, 8  6 = 2 or 8  2 = 6
How can you state those relationships in abstract terms? 
If x is some number and:
x + y = 0
then y is called an inverse (w.r.t. addition) of x
Then it follows from the same definition that x is an inverse of y. Now, what you need to prove is that inverses are unique. I.e. if for some given x
x + y = 0
and also
x + z = 0
you necessarily have y = z.
So, it then follows that the inverse of the inverse of x is x and it can't be anything else than x.
Then, if we denote the inverse of x by
x, we can prove that:
x = (1)*x
THis is because:
x + (1)*x =
1*x + (1)*x =
(1 + (1))*x =
0*x = 0
Here we have used that 1 is the inverse of 1.
So, (1)*x satisfies the criterium the inverse of x which we always denote as
x must satisfy and therefore
x = (1)*x
Then the fact that taking twice the inverse yields the same number implies that:
(1)*(1) = 1 
i agree with all of it but still don't see how
X + B = C
we can simply solve for B by simply multiplying the whole equation by B^1 which we note as B because????
(X + B = C)B^1
B cancels out
X = B^1 C
what allows us to say that B^1 is equal to B 
You are confusing terms:
Inverse is not the reciprocal. You are using reciprocal (B^1) is reciprocal.
Now it is confusing, because the inverse operation to multiplication is division, and the inverse to division is multiplication
http://www.mathsisfun.com/definitions/inverseoperation.html
Watch the usage to "inverse", a lot of folks really mean reciprocal when they use it.