Question

Determine if the following statement is true or false.

If it is true, explain how you know.

If it is false, give a counterexample to prove it is false.

Make sure to use full and complete sentences in your explanations.

The opposite of the opposite of a negative number is a positive number.

Answer 1

i would think that the 'opposite of the opposite of' is the number itself

Answer 2

So for -5 it would be -5.

Answer 3

it is false because:
starting from the number x (with x<0); take the opposite by multiplying it by (-1), getting (-x), a positive number; then take again the opposite of this new number by multiplying it by (-1), getting (x), a negative number.

In other words, if you take the opposite of a number "x" once, three times, five times, etc. , then the result is the same number but with the opposite sign (e.g. 5 becomes -5). While if you take the opposite of a number "x" twice, four times, six times, etc., then the result is exactly the same starting number "x" (5 rests 5).