(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I just want to show that given x<0, [tex]\frac{x-1}{x-2} <1[/tex].

3. The attempt at a solution

I don't know why I am having trouble with this! I feel like this is so easy!

So if x<0, then we know [tex]x-1<-1, x-2<-2 [/tex]. So

[tex]\frac{-1}{2}<\frac{1}{x-2}[/tex] and [tex]\frac{x-1}{x-2}<\frac{-1}{x-2}[/tex].

I can't seem to get a good upper bound on [tex]\frac{1}{x-2}[/tex] that makes the entire thing less than one. Am I doing something illegal? Because now it looks like I should want to get[tex]\frac{1}{x-2} <-1[/tex] to make it all less than one, but clearly that is not true.

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# Homework Help: Inequalities and bounds

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