What is the value of $-(-6)$?

Question

I know this is not absolute value, so what do the parentheses mean? If it was absolute value, it would have lines so I can rule that out.

And I guess I should mention, the question I was asked is "Enter the opposite of this number in the box." So, that's the context.

$-(-6)$

Answer 1

This means negative, negative $6$. As you probably know negative times negative is positive, so this is simply the value $6$ (positive six). The reason for the parenthesis is that the convention is that we do not have multiple operation signs in a row, e.g. signs like "$+$","$-$", and "$\times$". In a way you can say that every two negatives "cancel out", so

$$\require{cancel}-(-6) = \cancel{-}(\cancel{-}6) = \fbox{6}.$$

Now to answer the added question on what the "opposite number" is, I'm assuming that it is meant "the negative of the number." The question then is "What is the negative of $-(-6)$"? Since we have already resolved that $-(-6) = 6$, this question is the same as "What is the negative of $6$?", which is simply $-6$.

Answer 2

I think a lot depends on context.

If by $-6$ you are referring to the additive inverse of $6$ then $-(-6)$ is the additive inverse of the additive inverse of $6$

$4-(-6)$ however is slightly different. Here the first $-$ means subtract defined as adding the additive inverse. To be precise $4+-(-6)$ where the first $-$ now refers to the additive inverse.

There may be other contexts I'm unaware of. Hope that helps.

Answer 3

Remember that a negative number times a negative number is negative.

If you see $-(x)$ that's a short way of writing $(-1) \times x$, that is, "minus one" or "negative one" multiplied by $x$. In this particular case we have $x = -6$, so then $(-1) \times (-6) = 6$.

The parentheses in this case are for clarity: compare $--6$. Without the proper typesetting, that can look like one very long dash, instead of two minus signs. (In other cases, parentheses override operator precedence, plus they also have other mathematical uses that are not relevant to your question here--as for "minus one" versus "negative one", that's another can of worms altogether).