A questions about Cancelling out brackets.

[evosy1978]

Hello all, I am new here and I am 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

 

[Borek]

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.

 

[micromass]

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:

$$\begin{eqnarray*}<br /> 2x-(x+3)<br /> & = & 2x+(-1)*(x+3)\\<br /> & = & 2x + (-1)x + (-1)*3\\<br /> & = & 2x-x-3<br /> \end{eqnarray*}$$

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