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March 28, 2017

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solve inequalite place in interval notation

4-x/x-6<=0

  • algebra - ,

    f(x)=(4-x)/(x-6)

    First make a sketch of the equation (equality).

    As x -> ± &infin, f(x) approaches -1.
    There is also a vertical asymptote at x=6, approaching +∞ at 6- and -∞ at 6+. Therefore the function is discontinuous at that point.

    The one zero is at x=4, where the function crosses from negative to positive.

    If you have the sketch in front of you, it would be easy to find the places where the function is negative (≤0):
    from -∞ to 4, and from 6+ to ∞.

    If you need help putting that in interval notation, please post.

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