How do you know the opposite of a nonzero integer?

An Integer is defined as a positive or negative whole number or zero.

Now, a non zero integer means an integer that is not zero.This means examples of non zero integers are -1, +1, -2, +2 e.t.c.This means same numbers with opposite signs are the same distance from zero on either side of the number line.Since we are looking for opposite of a non zero integer, all we need to do is to change the sign from positive to negative or from negative to positive as the case may be.

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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
5the opposite is -5

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