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A questions about Cancelling out brackets.

  1. Jan 6, 2012 #1
    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
     
  2. jcsd
  3. Jan 6, 2012 #2

    Borek

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    Staff: Mentor

    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.
     
  4. Jan 6, 2012 #3

    micromass

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    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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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