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Absolute value inequalities *Grr* help appreciated :D Watch

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    Hi,

    Inequalities are an absolute pain, but add absolute values and well... :rolleyes:

    Anyway, I've just made up a question so the question I really need to answer isn't answered for me (though, that would be great-it wouldn't really help a great deal!)
    So, if we need to solve the following inequality:

    x^2 - 3x / |x+2| <0


    I begin with writing:

    0 < x^2 - 3x / |x+2| &lt;0
    Should I multiply each side by (x+1) ?? because after this step, I'm completely unsure what to do :/

    Any help appreciated!
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    LOL, no one?
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    Everything is incorrect.

    Hint: If x = -2 ?

    Remember you can use positive real numbers without affecting the inequality, viz. if a < b and x is positive ax < bx where as negative x gives ax > bx.
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    (Original post by DeanK22)
    Everything is incorrect.

    Hint: If x = -2 ?

    Remember you can use positive real numbers without affecting the inequality, viz. if a < b and x is positive ax < bx where as negative x gives ax > bx.
    Nope. Nothing. I'm officially lost
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    (Original post by dream123)
    Nope. Nothing. I'm officially lost
    If x = -2 we have |x+2| = 0 which better not be in the denominator.

    As |y| => 0 for all y (and > 0 if y =/= 0 ) we multiply by the positive |x+2| to obtain

     \displaystyle x^2 - 3x &lt; 0 \iff x(x-3) &lt; 0

    That occurs iff x < 0 and x-3 > 0 or x > 0 and x - 3 < 0

    Spoiler:
    Show
    Generally if a > 0 the quadratic ax^2 + bx + c is less than zero in the interval between its root if multiple roots exist.
 
 
 
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