1. ## 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?

2. 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.

3. 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.

4. 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.

5. 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.

6. Hi Pupil,

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

7. 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!

8. 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.