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Drawing graphs

  1. Mar 3, 2013 #1
    find the values of x for which

    [itex] x + 4 > \dfrac{2}{|x+3|} [/itex]

    as the | x + 3 | is positive I thought it would be okay to just bring it over so:

    [itex] (x+4)(x+3) > 2 [/itex] solving this, I get x > -2 and x < - 5

    however drawing a sketch of the original question shows that the only value needed is x > - 2

    my question is why doesn't my method work, and is there a way to do this algebraically without any graph drawing?
     
  2. jcsd
  3. Mar 3, 2013 #2

    eumyang

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    Homework Helper

    It may be okay to "just bring it over," but that does not mean you can drop the absolute value symbol. You still need them:
    [itex] (x+4)|x+3| > 2 [/itex]

    Make a sign chart. Find values that make the original inequality 0 or undefined, and plot them on a number line:
    Code (Text):
    <--------+--------+--------+-------->
            -5       -3       -2
    Test a value in each interval to see if the inequality holds.
     
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