inequality question?

Question

anonymous · Answer

$$5- 4x \div 3x ^{2} - x - 4 < 4$$

e.mccormick · Answer

Going to depend on what is divided by what.  Generally, inequalities are solved in the same basic way as equalities.  Get x alone, there is the answer.  The caveat is that inequalities have different rules for getting x alone.  Multiplying or dividing by a negative flips the inequality.

anonymous · Answer

ughh, what ?

anonymous · Answer

@Luis_Rivera  what? for question or @e.mccormick  comment cause i didn't understand what he meant?

anonymous · Answer

and (5-4x)/(3x2-x-4)<4

e.mccormick · Answer

Well, that was my question part.
$$\frac{5-4x}{3x^2-x-4}<4$$

anonymous · Answer

thats the question

anonymous · Answer

i am solving this for half an hour but no big success

anonymous · Answer

lol

anonymous · Answer

i only reached till this point 
(21-12x2)/(3x2-x-4)<0

anonymous · Answer

@Luis_Rivera  don't laugh man i have exam in 4 hours!!

e.mccormick · Answer

Did you ever try factoring the bottom?

anonymous · Answer

no

e.mccormick · Answer

Get to fully factored form, then make a truth table.

anonymous · Answer

@e.mccormick k factoring the bottom is done now we have 3 roots 
$$\pm \sqrt{7}\div2$$

anonymous · Answer

-1 and 4/3

anonymous · Answer

u mean the number line table

e.mccormick · Answer

OK, so those points would be false no matter what.  They are DNEs.

e.mccormick · Answer

$$\frac{3(7-4x^2)}{(3x-4)(x+1)}$$

e.mccormick · Answer

Now, that top does factor as a difference of squares if you use $\sqrt{7}$ as one of them.

anonymous · Answer

k solving this i got 
$$ x \in (-\infty,-\sqrt{7}\div2)\cup(-1,\sqrt{7}\div2)\cup(4\div3,infty)$$

anonymous · Answer

is this correct

e.mccormick · Answer

I have not worked the truth table.  As long as your holes are avoided and it is always <0, it should be correct.  Did you run up test points in those ranges?

anonymous · Answer

yes its satisfying the equation

e.mccormick · Answer

Good, good.  yah, as long as your DNE spots are out of the answer space and the test points between all critical points are in, then you should be safe.  I did a writeup on somethign similar for domains of roots.

anonymous · Answer

thanks

e.mccormick · Answer

np.  The paper is a page and a half.  It explains the concept for the truth table.  The thing you had an issue with here was really just not doing the facotring.   Once it is factored, then the concept of a truth table is easier to apply.

anonymous · Answer

ohh

anonymous · Answer

thanks @e.mccormick  and buy guys

e.mccormick · Answer

Ah, I think Luis_Rivera was looking at mine with a "Huh" type reaction.  Not yours.  Or if yours, the same question I had, what is divided.