I understand $-x$ to be the additive inverse of $x$ and vice versa. But looking at an example in my book, it says $-x$ = $-(x)$. Is that quite literally a result of the fact that negative $x$ is equal to the negation of $x$ or is there an alternative reasoning to it?

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    $\begingroup$ I think it's nothing. Just $x=(x)$. $\endgroup$ – Michael Rozenberg Aug 26 '17 at 17:38
  • $\begingroup$ I don't believe having the addition of parentheses adds anything to it I'm afraid. I agree with @MichaelRozenberg and it would only apply if there is more information within the brackets $\endgroup$ – Morgan Aug 26 '17 at 17:40
  • $\begingroup$ I think it's noting that because if you have say 5-6 you can do 5+(-6) and such. just another way of notating the fact that subtraction allows you to switch signs in parentheses. $\endgroup$ – user451844 Aug 26 '17 at 17:42
  • $\begingroup$ which if x was an expression would help. $\endgroup$ – user451844 Aug 26 '17 at 17:43
  • $\begingroup$ @Morgan The example was to show the place value expansion of -741, so it was shown $(-741) = -(741) = -(700 + 40 + 1) = (-700) + (-40) + (-1).$ Which is fine but I don't understand what is the general reason for going from (-741) to -(741). $\endgroup$ – salman Aug 26 '17 at 17:44

It's just multiplicative associative property. $$-x=-1\cdot x$$ And by the aforementioned property, $$-1\cdot x=-(x)$$ Thus, $$-x=-(x)$$


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