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Math Help - inequality

  1. #1
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    inequality

    I have a inequality

    3 - x / 2 > 7

    I am to get x on the left on its own, however I am not asked to see if the LHS would then be greater than 7?

    My method;

    First get rid of the denominator 2

    3 - x > 2 x 7

    Then move 3 to the RHS

    x > 14 - 3

    x > 11

    Now if I put 11 in the inequality the answer is - 2.5

    so the result; - 2.5 > 7 is wrong?

    Is my method wrong or am I just to show how to get X on it's own?

    Thanks

    David
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: inequality

    x > 11


    11 is not greater than 11 !
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  3. #3
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    Re: inequality

    Quote Originally Posted by David Green View Post
    I have a inequality

    (3 - x)/2 > 7

    I am to get x on the left on its own, however I am not asked to see if the LHS would then be greater than 7?

    My method;

    First get rid of the denominator 2

    3 - x > 2 x 7

    Then move 3 to the RHS

    - x > 14 - 3

    - x > 11

    x < -11
    ...
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  4. #4
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    Re: inequality

    Quote Originally Posted by skeeter View Post
    ...
    I see it know, X I knew had to be on it's own, but I didn't think about changing the sides to get X on it's own?

    -x > 11 here X is not alone

    x < - 11 here X is alone

    Thanks

    David
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  5. #5
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    Re: inequality

    Quote Originally Posted by David Green View Post
    I have a inequality

    3 - x / 2 > 7

    I am to get x on the left on its own, however I am not asked to see if the LHS would then be greater than 7?

    My method;

    First get rid of the denominator 2

    3 - x > 2 x 7

    Then move 3 to the RHS

    x > 14 - 3

    x > 11

    Now if I put 11 in the inequality the answer is - 2.5

    so the result; - 2.5 > 7 is wrong?

    Is my method wrong or am I just to show how to get X on it's own?

    Thanks

    David
    Obtain a positive x on one of the two sides, viz

    \frac{3-x}{2}>7

    Double both sides

    \frac{2(3-x)}{2}>2(7)

    3-x>14

    Add x to both sides

    3-x+x>14+x

    3>x+14

    x+14<3

    Subtract 14 from both sides

    x+14-14<3-14

    x<-11
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