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Math Help - Solve linear equation

  1. #1
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    Feb 2010
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    Solve linear equation

    Hi,
    I found the following practice problem online. I tried to solve it by doing what I was taught at school to solve such an equation-moving the variable to one side and the constants to another and I ended up with this:
    5(-3x - 2) - (x - 3) = -4(4x + 5) + 13
    -15x -10 -x + 3 = -16x -20 + 13
    -15x -x +16x = 10 -3 +13
    0 = 20

    Obviously wrong!

    But actually solution does this:
    5(-3x - 2) - (x - 3) = -4(4x + 5) + 13
    -15x -10 -x + 3 = -16x -20 + 13
    -16x -7 = -16x -7
    Multiply both sides by 16x + 7 and get:
    0=0

    Why does the conventional method not yield results when that is how I solve all my linear equations? How do I know when to apply the second method?

    Thanks.
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  2. #2
    Senior Member
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    Jul 2009
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    Melbourne
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    I'm really confused by your method and I'm sure you are confusing yourself. Make it easier by taking away 1 thing at a time:

    Expand brackets to get:

    -15-10-x+3=-16x-20+13

    Get the x values to the left side.

    -15-10+15x+3 = -20+13 I added 16x to both sides.

    Now the rest should be simple.

    You are doing this:

    -15-10-x+3 +16x=x-20+13

    See how you just wrote "16x" you may as well add it straight away to get yourself not confused...
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  3. #3
    MHF Contributor

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    Quote Originally Posted by math934 View Post
    Hi,
    I found the following practice problem online. I tried to solve it by doing what I was taught at school to solve such an equation-moving the variable to one side and the constants to another and I ended up with this:
    5(-3x - 2) - (x - 3) = -4(4x + 5) + 13
    -15x -10 -x + 3 = -16x -20 + 13
    -15x -x +16x = 10 -3 +13
    Here's your error. You added 10- 3 to both sides but the right side is -20+ 13. You dropped the -20.

    0 = 20
    You should have 0= 20- 20 which is the same as 0 = 0.

    Obviously wrong!
    But actually solution does this:
    5(-3x - 2) - (x - 3) = -4(4x + 5) + 13
    -15x -10 -x + 3 = -16x -20 + 13
    -16x -7 = -16x -7
    Multiply both sides by 16x + 7 and get:
    0=0

    Why does the conventional method not yield results when that is how I solve all my linear equations? How do I know when to apply the second method?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2010
    Posts
    4

    re:

    HallsofIvy,
    I knew it,I knew it, I knew it. This is my problem. I always make the silliest mistake and end up messing up the entire problem

    Thanks very much for your help.
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