# Inequalities help.

• October 8th 2010, 08:03 PM
Pupil
Inequalities help.
The equation is $x^3-6x^2+5x-12 > 0$

I got my x-intercepts or the root of the equation after factoring: $(x+1)(x-3)(x-4)$

Now how exactly would I solve this by putting it in this form:

$-1 < x < 3$ and $x > 4$ or $x > -1$ and $3 < x < 4$

I am confused as to which one is the right answer, and can you please explain how to correctly choose and determine it?

• October 8th 2010, 08:08 PM
Educated
Quote:

Originally Posted by Pupil
The equation is $x^3-6x^2+5x-12 > 0$

I got my x-intercepts or the root of the equation after factoring: $(x+1)(x-3)(x-4)$

$x^3-6x^2+5x-12 > 0$
I think you factored it wrong somewhere, this equation cannot be factored into such a simplistic form.

If it were $x^3-6x^2+5x+12 > 0$ then you factored it correctly.
• October 8th 2010, 08:48 PM
Pupil
Quote:

Originally Posted by Educated
$x^3-6x^2+5x-12 > 0$
I think you factored it wrong somewhere, this equation cannot be factored into such a simplistic form.

If it were $x^3-6x^2+5x+12 > 0$ then you factored it correctly.

Yeah it's +12, I made a typo.

So which would be the answer and how I about do I go finding the answer for future inequalities? I have read dozens of articles online and nothing shows any way to go about solving these.
• October 8th 2010, 09:21 PM
Educated
Well i'm not good at explaining things but I'll try to explain as best as I can:

It's the x^3 that tells us which answer it is. It tells us that as x goes to positive infinity, so does y. But if it were -(x^3), then this would tell us that as x goes to positive infinity, y goes to negative infinity.

Since the x^3 is positive, x would have to be larger than the largest root because it goes to infinity, and so $x > 4$. When we know this, we know the rest.

Sorry I'm not better at my explanations.
• October 8th 2010, 09:39 PM
Pupil
Quote:

Originally Posted by Educated
Well i'm not good at explaining things but I'll try to explain as best as I can:

It's the x^3 that tells us which answer it is. It tells us that as x goes to positive infinity, so does y. But if it were -(x^3), then this would tell us that as x goes to positive infinity, y goes to negative infinity.

Since the x^3 is positive, x would have to be larger than the largest root because it goes to infinity, and so $x > 4$. When we know this, we know the rest.

Sorry I'm not better at my explanations.

I am writing this down in my notes, thanks.

But is there like any practical way to apply your theory to other questions I may have? I thought that too, but as I was looking through my examples my book didn't explain it at all too well and only gave a couple of examples.
• October 8th 2010, 10:25 PM
harish21
Hi Pupil,

You may want to have a look at this thread. Thanks to MHF member Krizalid,this attachment contains nice explanations about inequalities.
• October 8th 2010, 10:32 PM
Pupil
Quote:

Originally Posted by harish21
Hi Pupil,

You may want to have a look at this thread. Thanks to MHF member Krizalid,this attachment contains nice explanations about inequalities.

Thank you Harish, this might be what I've been looking for!
• October 8th 2010, 10:40 PM
Pupil
Quote:

Originally Posted by harish21
Hi Pupil,

You may want to have a look at this thread. Thanks to MHF member Krizalid,this attachment contains nice explanations about inequalities.

Unfortunately Harish, it wasn't exactly what I was looking for. While it may be a greatly written guide, it seems like the general articles I've found all over the net explaining inequalities and I haven't gotten that deep in this topic yet.

All I really am looking for is how to determine which one is the answer and why, the way my text book explains it is much too vague with too few examples.