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# How to combine inequalities

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1. How would I combine -2<x-1<0 and 1>(1/x+2)>1/3 to get Mod(x-1/x+2) <2? Is there a general rule on how to do this? )
2. We have:

.

And

.

Can you take it from here?
3. Thank you!!!
4. (Original post by Lunu)
How would I combine -2<x-1<0 and 1>(1/x+2)>1/3 to get Mod(x-1/x+2) <2? Is there a general rule on how to do this? )

2. I would write:

and then since all quantities are non-negative in both inequalities, we can multiply them to get:

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