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Rational Inequalities

  1. Oct 23, 2012 #1
    My final answer matches that of the text book, but do I need to change the < to > at any point as I solve this? I ask because, if I assume x is 1 (until I solve for x), then the question statement and parts of the solution are made untrue.

    1. The problem statement, all variables and given/known data

    Solve the following for x [itex]\in\mathbb{R}:[/itex] [itex]\frac{x}{2x-1}<-2[/itex]

    2. Relevant equations

    3. The attempt at a solution

    [itex]\frac{x(2x-1)^2}{2x-1}<-2(2x-1)^2[/itex]
    [itex]x(2x-1)<-2(4x^2-4x+1)[/itex]
    [itex]2x^2-x<-8x^2+8x-2[/itex]
    [itex]10x^2-9x+2<0[/itex]
    [itex](5x-2)(2x-1)=0[/itex]
    [itex]x=\frac{2}{5}[/itex] or [itex]\frac{1}{2}[/itex]
    [itex]\frac{2}{5}<x<\frac{1}{2}[/itex]
     
  2. jcsd
  3. Oct 23, 2012 #2

    tiny-tim

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    hi odolwa99! :smile:
    but 1 isn't between 2/5 and 1/2,

    so why is that a difficulty? :confused:
     
  4. Oct 23, 2012 #3
    Yeah, I'm just double checking my work so I can be absolutely sure I'm correct at all steps. Thanks for looking at it for me.
     
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