Rational Inequalities

1. Oct 23, 2012

odolwa99

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 $\in\mathbb{R}:$ $\frac{x}{2x-1}<-2$

2. Relevant equations

3. The attempt at a solution

$\frac{x(2x-1)^2}{2x-1}<-2(2x-1)^2$
$x(2x-1)<-2(4x^2-4x+1)$
$2x^2-x<-8x^2+8x-2$
$10x^2-9x+2<0$
$(5x-2)(2x-1)=0$
$x=\frac{2}{5}$ or $\frac{1}{2}$
$\frac{2}{5}<x<\frac{1}{2}$

2. Oct 23, 2012

tiny-tim

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

so why is that a difficulty?

3. Oct 23, 2012

odolwa99

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.