-1

This is kinda embarrassing but I'm having trouble with a fairly basic inequality. This is what I have so far:

x - 4/abs(x+2) < -1 x - 4 < -1(x+2)

case 1, if x+2 >= 0 or x >= -2

x - 4 < -x - 2 2x < 2 x < 1

so [-2, 1)

case 2, if x+2 < 0 or x < -2

x - 4 < -1*-(x+2) x - 4 < -1*(-x - 2) x - 4 < x + 2

and this is where I'm stuck, how can I solve for x? I know that the answer should be negative infinity up to but not including one so would something like this work:

0x < 6 x < 6/0, therefore x has to be infinity? Though it doesn't really show that it's negative infinity so I'm a bit confused.

Is there something really simple that I'm missing or am I going about it in a dumb way?

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Sorry, this is the right site for this type of question. MathOverflow is directed at research level mathematics. Please have a look at the first two sections of the FAQ (mathoverflow.net/faq). In particular, mathoverflow.net/faq#homework lists some other math forums where your question may be a better fit. I'll give you a little push: is x=-3 a solution? How about x=-4? You can just plug them in and check. Based on that, can you come up with a guess for which numbers less than -2 are solutions? – Anton Geraschenko♦ Mar 27 2010 at 6:15
If you just need the answer, wolframalpha can solve these. However, if you grow to depend on computers for this level of thing, then you will never achieve the speed of thought that one needs to have for "real" math. – Kevin O'Bryant Mar 27 2010 at 18:07

closed as off topic by Anton Geraschenko♦♦ Mar 27 2010 at 6:15

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