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- Oct 15th 2013, 05:17 AM #1

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- Oct 15th 2013, 06:07 AM #2

- Oct 15th 2013, 06:17 AM #3

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- Oct 15th 2013, 06:32 AM #4
## Re: Help please

Let's look at the first one. For starters if $\displaystyle |y| \leq k$ the we know that $\displaystyle -k \leq y \leq k$. So your first problem becomes:

$\displaystyle \left | \frac{x}{x - 1} \right | \leq 1 \implies -1 \leq \frac{x}{x - 1} \leq 1$

What can you do with this?

-Dan

- Oct 15th 2013, 07:38 AM #5

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## Re: Help please

Keep track of the direction of the inequalities. They are reversed if you multiply the inequality by a negative number. So, if you want to multiply across the inequality by $\displaystyle x-1$, you need to consider two cases: when $\displaystyle x-1>0$ and when $\displaystyle x-1<0$.