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Thread: Inequality

  1. #1
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    Inequality

    Help!! I need help finding x.
    2x (7 + x) < x

    2x - 7 - x <= x
    x - 7 <= x

    The x cancels out, so is the answer that circle with the diagonal line through it?
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  2. #2
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    Quote Originally Posted by ashleydevos View Post
    Help!! I need help finding x.
    2x (7 + x) < x

    2x - 7 - x <= x
    x - 7 <= x

    The x cancels out, so is the answer that circle with the diagonal line through it?
    $\displaystyle x-7 \le x$

    you did not finish, subtract $\displaystyle x$ from both sides ...

    $\displaystyle -7 \le 0$

    a true statement ... therefore the inequality is true for all $\displaystyle x$
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  3. #3
    Super Member Bacterius's Avatar
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    $\displaystyle 2x - (7 + x) \leq x$

    $\displaystyle 2x - 7 - x \leq x$

    $\displaystyle x - 7 \leq x$

    $\displaystyle -7 \leq 0$

    So this equality holds for any $\displaystyle x$, because $\displaystyle -7$ is indeed smaller than $\displaystyle 0$.

    EDIT : erf Skeeter beat me to it
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  4. #4
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    How do you write it in interval notation then? [-7<= ∞)???
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  5. #5
    Super Member Bacterius's Avatar
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    No, no !

    Regardless of the value of $\displaystyle x$, the inequality holds, so I guess you could write this $\displaystyle x = \mathbb{R}$, or :

    $\displaystyle \forall x \in \mathbb{R}$, $\displaystyle 2x - (7 + x) \leq x$

    A less elegant but more direct way to write it could be : $\displaystyle x = (-\infty, +\infty)$, $\displaystyle x \in \mathbb{R}$.
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