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How to Break parenthesis

  1. Sep 14, 2009 #1
    1. The problem statement, all variables and given/known data
    I want to solve this equation: 8x - (3x + 2) = 2x - 10


    2. The attempt at a solution
    I tried this:
    8x - (3x + 2) = 2x - 10

    (3x + 2) = 2x - 8x -10
    (3x + 2) = -6x - 10

    I know how to break parenthesis when there are no signs between a number and the parenthesis...but the exercise has a minus sign between 8x and (3x + 2) which separates them, how do I solve this?
     
  2. jcsd
  3. Sep 14, 2009 #2
    8x - (3x + 2) = 8x + (-1)*(3x+2)

    Does that help?
     
  4. Sep 14, 2009 #3
    Yes that helped! This is what I did:

    8x - (3x + 2) = 2x - 10

    8x - 1(3x + 2) = 1(2x - 10)

    8x - 3x -2 = 2x - 10

    (Now I move all variables together)
    8x - 3x -2x = -2 - 10

    3x = -12

    3x/3 = -12/3

    (3's are canceled)
    x = -4

    Thanks alot! I forgot I could multiply by 1 so the exercise didn't change

    EDIT: SOLVED!
     
    Last edited: Sep 14, 2009
  5. Sep 14, 2009 #4
    That's the correct way to distribute! But watch out when going from:

    8x - 3x -2 = 2x - 10

    to

    8x - 3x -2x = -2 - 10

    The sign on your 2 needs to be fixed :)
     
  6. Sep 14, 2009 #5
    Alternatively:

    [itex] 8x-(3x + 2)=2x -10[/itex]

    [itex]8x-3x-2=2x-10[/itex]
     
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