A questions about Cancelling out brackets.

  • Thread starter evosy1978
  • Start date
  • #1
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Hello all, Im new here and Im currently studying IGCSE Math. Hope you can explain something to me.

I have what you may think is a basic question.... I just wanted to query it.

Its to do with cancelling out brackets.

so
2x-(x+3) = 2x-x-3 = x-3

I think I understand why the +3 inside the brackets changes to a -3. (its because of the minus before the brackets)

So what about the +x inside the brackets aswell? why does this not change to a -x aswell?

and therefore ending up with 2x - -x -3 and then 2x + x - 3

2x - (x+3)
2x - -x -3
2x + x -3 = 3x-3

I hope I have explained my way of thinking clearly? (even though I know its wrong could someone explain why its wrong)

Thanks
 

Answers and Replies

  • #2
Borek
Mentor
28,701
3,188
It did change:

-(x+3) = -x -3

Note that both signs (of x and of 3) changed.

You are trying to change it for the second time.
 
  • #3
22,089
3,297
I don't really like rules like "if there is a - in front of the bracket, change the signs". You have to be sure to understand why it is the case.

It simply follows from distributivity:

[tex]
\begin{eqnarray*}
2x-(x+3)
& = & 2x+(-1)*(x+3)\\
& = & 2x + (-1)x + (-1)*3\\
& = & 2x-x-3
\end{eqnarray*}
[/tex]

So instead of remembering a silly rule, just replace the - by (-1)* and work it out by distibutivity.
 

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