# Logic proof question

• Sep 22nd 2009, 06:47 PM
p00ndawg
Logic proof question
if $\displaystyle (x/(x-1)) \leq 2$, then $\displaystyle x < 1$or $\displaystyle x \geq 2$.

Im not sure how to prove this.

I tried this method here from the user xalk, but it didnt seem to work for this question even though this one is similar.

http://www.mathhelpforum.com/math-he...gic-proof.html
• Sep 22nd 2009, 07:17 PM
pickslides
Here's a start

$\displaystyle \frac{x}{x-1} \leq 2$

$\displaystyle x \leq 2(x-1)$

$\displaystyle x \leq 2x-2$

Now solve for x.
• Sep 22nd 2009, 07:20 PM
artvandalay11
Quote:

Originally Posted by p00ndawg
if $\displaystyle (x/(x-1)) \leq 2$, then $\displaystyle x < 1$or $\displaystyle x \geq 2$.

Im not sure how to prove this.

I tried this method here from the user xalk, but it didnt seem to work for this question even though this one is similar.

http://www.mathhelpforum.com/math-he...gic-proof.html

So $\displaystyle \frac{x}{x-1}\leq 2$

What if x>1? Then $\displaystyle x\leq 2(x-1)\rightarrow x\leq 2x-2\rightarrow -x\leq -2\rightarrow x\geq 2$ So if x>1, x must be $\displaystyle \geq 2$

Try something similar for x<1