Logic proof question

**p00ndawg** · September 22nd 2009, 06:47 PM

if $(x/(x-1)) \leq 2$ , then $x < 1$ or $x \geq 2$ .

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

**pickslides** · September 22nd 2009, 07:17 PM

Here's a start

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

$x \leq 2(x-1)$

$x \leq 2x-2$

Now solve for x.

**artvandalay11** · September 22nd 2009, 07:20 PM

Originally Posted by p00ndawg

if $(x/(x-1)) \leq 2$ , then $x < 1$ or $x \geq 2$ .

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

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

Try something similar for x<1

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