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Math Help - Basic inequality problem

  1. #1
    Newbie
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    Apr 2009
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    Linear inequality problem(solved)

    Hello, I'm a new member and if I unknowingly made a mistake by posting in the wrong forum, I apologize. I've stumbled upon a problem while studying for a important test and I'd really like to understand it.

    I'm supposed to find out what x could be.

    (x-3)+x≥3(3-x)


    I got this:

    (x-3)+x≥3(3-x)
    2x-3≥9-3x
    2x≥12-3x
    -1x≥12
    x≥-12

    But the answer book says it's x≥2,4
    I think there's something wrong with my simplifying.
    Last edited by kappa; April 19th 2009 at 03:19 PM.
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  2. #2
    MHF Contributor
    Joined
    Mar 2007
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    Talking

    Quote Originally Posted by kappa View Post
    I'm supposed to find out what x could be.

    (x-3)+x≥3(3-x)
    The first step for solving this linear inequality will be to multiply things out and see what we've got:

    . . . . .(x - 3) + x > 3(3 - x)

    . . . . .x - 3 + x > 9 - 3x

    . . . . .2x - 3 > 9 - 3x

    Let's move everything over to one side:

    . . . . .5x - 12 > 0

    This is linear, so:

    . . . . .5x > 12

    . . . . .x > 12/5 = 2.4

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  3. #3
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    Quote Originally Posted by stapel View Post
    The first step for solving this linear inequality will be to multiply things out and see what we've got:

    . . . . .(x - 3) + x > 3(3 - x)

    . . . . .x - 3 + x > 9 - 3x

    . . . . .2x - 3 > 9 - 3x

    Let's move everything over to one side:

    . . . . .5x - 12 > 0

    This is linear, so:

    . . . . .5x > 12

    . . . . .x > 12/5 = 2.4

    Oooh, I subtracted 3x instead of adding. Much appreciated!!
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