Question

How do you know the opposite of a nonzero integer?

Answer 1

Answer with explanation:

The opposite of a non-zero integer means the additive inverse of the number.

It is found by adding a number to the given integer such that there sum is equal to the additive identity.

( Additive Identity--

The additive identity  is the value which when added to any number gives the resultant as the same number .

We know that the identity under addition is: 0

because ,

a+0=a for every a )

Let a be any non-zero integer and let b be the opposite of a.

i.e.

a+b=0

i.e.

b= -a

This means that the opposite of a non-zero integer is a non-zero integer with the same magnitude but different sign.

For example--

Opposite of -2 is: 2

and Opposite of 3 is: -3

Answer 2

The opposite of a non-zero integer can be found by just switching the sign.

example : 
2...the opposite is -2
-3...the opposite is 3
5....the opposite is -5

basically, they are opposites if they are the same distance away from 0, but on opposite sides of the number line