# 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

1. Writeacher

Use numbers.

6 + 2 = 8

Therefore, 8 - 6 = 2 or 8 - 2 = 6

How can you state those relationships in abstract terms?

2. Count Iblis

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

3. Very easy Math

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

4. bobpursley

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/inverse-operation.html

Watch the usage to "inverse", a lot of folks really mean reciprocal when they use it.

## Similar Questions

1. ### Another Problem...PLz Help COunt Iblis

Statements Reasons 1. 3x - 7 = -4 2. 3x - 7 + 7 = -4 + 7 3. 3x + 0 = -4 + 7 4. 3x + 0 = 3 5. 3x = 3 6. (1/3) 3x = 3 (1/3) 7. (1/3) 3x = 1 8. 1x = 1 9. x = 1 Is this problem about explaining each step?
2. ### Math

Using the definition of subtraction to determine the subtraction equations that are related to each of the following addition equation: a.8+7=n b.14+x=25 c.r+s=t my answers are this: a. n-7=8 b.x=25-14 c.t-s=r did I do these right?
3. ### MATH 156

What models can be used to help explain the concepts of addition and subtraction of rational numbers?
4. ### math

What inverse operation is needed for the first step in solving the equation 12+5x=22?
5. ### math

An eighth-grade student claims she can prove that subtraction of integers is commutative. She points out that if a and b are integers, then a-b = a+ -b. Since addition is commutative, so is subtraction. What is your response?
6. ### Math--1 question

Name the inverse operations for each of the following operations. a. addition b. division c. multiplication d. subtraction