7+(-7)=0  demonstrates the "additive inverse property"

Here's what you need to know:

THE ADDITIVE IDENTITY IS 0
There is just one "do-nothing" number for addition. 
This is 0 because when you add 0 to a number it "does 
nothing" for you get the same number back, so adding 
zero does nothing but give you IDENTICALLY the same 
number you started with. Every other number besides 0 
does something when you add it, but not 0.  So 0 is the 
additive identity.  (There is also a multiplicative 
identity, 1, because it does nothing when you multiply
by it.  So 0 is the additive identity, and 1 is the 
multiplicative identity.  But right now for this problem 
we only need to talk about the additive identity.)  

THE ADDITIVE INVERSE OF A NUMBER
The additive inverse is the "IDENTITY-MAKER", or in the 
case of addition, the additive inverse.  Every number has 
just one "IDENTITY-MAKER" number under addition. The 
number 7 has the IDENTITY MAKER -7 because when you add 
the number -7 to the number 7 that makes 0, which is the 
IDENTITY for addition. (There are also multiplicative 
inverses, which are "ONE-MAKERS". (The multiplicative 
inverse of  is  because when you multiply 
 by  you get the IDENTITY for multiplication. 
But right now for this problem we only need to talk about 
the additive identity and the additive inverse). 

Question:  What do you have to add to 7 to make zero,
           (which is the "do-nothing" number for addition?)  

Answer: You need to add -7 to make zero, the do-nothing number 
        for addition.

Therefore -7 is the additive inverse of 7.  And 0 is the
additive identity.

So when you add the ADDITIVE INVERSE -7 to 7, you get 
the identity 0, or 7+(-7)=0   

Another word for "ADDITIVE INVERSE" is "OPPOSITE", formed 
by changing the sign.

---

Question:  What do you have to multiply 7 by to make one,
           (which is the "do-nothing" number for 
           multiplication?)  

Answer: You need to multiply  by  to make 
        one, the do-nothing number for addition.

Therefore  is the muclipicative inverse of 7.  And 1 is the
additive identity.

So when you multiply 7 by the MULTIPLICATIVE INVERSE of 7, you get 
the identity 1, or x   

Another word for "MULTIPLICATIVE INVERSE" IS "RECIPROCAL",
formed by INVERTing it. (That's where they got the name 
"INVERSE" in the first place, but they borrowed it for
addition too. 

TMI?  Depends on how deep your teacher goes!
Edwin