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Math Help - 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?
    x-7 \le x

    you did not finish, subtract x from both sides ...

    -7 \le 0

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

    2x - 7 - x \leq x

    x - 7 \leq x

    -7 \leq 0

    So this equality holds for any x, because -7 is indeed smaller than 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 x, the inequality holds, so I guess you could write this x = \mathbb{R}, or :

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

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