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Thread: inequality

  1. #1
    ADY
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    inequality

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

    is this right?

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

    $\displaystyle \frac{x}{2} > 4$

    $\displaystyle x < 8$

    ?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by ADY View Post
    $\displaystyle 3 - \frac{x}{2} > 7$

    is this right?

    $\displaystyle \frac{x}{2} > 7 - 3$
    No

    From $\displaystyle 3 - \frac{x}{2} > 7$

    Add $\displaystyle \frac{x}{2}$ to both sides

    $\displaystyle 3 > 7 + \frac{x}{2}$

    Subtract 7

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

    $\displaystyle -4 > \frac{x}{2}$

    Multiply by 2 (positive number therefore does not change the sense of the inequality)

    $\displaystyle -8 > x$
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  3. #3
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by ADY View Post
    $\displaystyle 3 - \frac{x}{2} > 7$

    is this right?

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

    $\displaystyle \frac{x}{2} > 4$

    $\displaystyle x < 8$

    ?
    No, when multiplying or dividing by a negative number you need to change the direction of the inequality although it is usually easier to use the method running-gag used
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