# Thread: Help with Inequations in Module

1. Hi, I'm new to this forum so I would like to apologize in advance if I mess up with anything ^^

I've been having trouble with Module inequations, specially one that has been bugging me for quite some time. Please keep in mind that English is my second lenguage, so any mathematical terms that I might use is roughly a translation from my native lenguage (portuguese)

Ok, then here's the Inequation:

|x-1| - |x+2|> x

I don't know how should I begin when trying to approach a solution, any help is really appreciated ^^

2.

3. I think the best way to go about this is to consider all of the possibilities for the values of |x-1| and |x+2|. We have:

|x-1| = x-1 if x-1 ≥ 0, i.e. if x ≥ 1
|x-1| = 1-x if x-1 ≤ 0, i.e. if x ≤ 1

|x+2| = x+2 if x+2 ≥ 0, i.e. if x ≥ -2
|x+2| = -x-2 if x+2 ≤ 0, i.e. if x ≤ -2

Now, in general, what are the possibilities for x? Well, if x ≥ 1, then x ≥ -2, so we have:

|x-1| = x-1, |x+2| = x+2

If x ≤ 1, we may have x ≥ -2. If so, we have:

|x-1| = 1-x, |x+2| = x+2

Otherwise, x ≤ -2, and:

|x-1| = 1-x, |x+2| = -x-2

So now plug this information into the inequality. For example, if x ≥ 1, we want to solve:

(x-1)-(x+2) > x
-3 > x

Well, this contradicts x ≥ 1, so evidently there are no solutions with x ≥ 1. Now do the same thing for -2 ≤ x ≤ 1 and x ≥ -2.

4. It worked! Thanks a lot man! ^^

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