Precal
posted by Abi .
Please help.
I'm having a lot of trouble with solving inequalities and graphing them
solve the inequality and graph the solution on the real number line
x^2+x6/x
I got SS: infinity to 3 including 3 union 2 to infinity including 2
is that right?

Precal 
Abi
EDIT WHERE INEQUALITY IS GREATER THAN OR EQUAL TO ZERO

Precal 
Damon
do you mean
6/x
or do you mean
(x^2+x6)/x
???? 
Precal 
Abi
Sorry i should have put that in parenthesis
(x^2+x6)/x greater than or equal to 0 
Precal 
Damon
well we know that when x = 0, it is 6/0
which is undefined but is huge positive for x small negative and huge negative for x small positive, so sketch that on your graph.
for x large positive x + 1  (6/x) looks like y = x so draw a line sloping up at 45 degrees for large positive x
for x large negative x + 1 (6/x) looks like y = x again so sloping down at 45 degrees in quadrant 3
Now, where is it zero?
x^2 + x  6 = 0
(x3)(x+2) = 0
x = 2 or x + +3
well, that does it, look at your graph sketch
it is positive from x = 2 to x = 0
it is positive from x = 3 to x = +oo 
whoops typo 
Damon
(x+3)(x2) = 0
x = 3 or x = +3
positive from x = 3 to x = 0
positive from x = +2 to x = +oo 
Precal 
Abi
Isn't it x^2+x6 = 0
(x+3)(x2) = 0?
x = 3 or x= +2? 
Precal 
Damon
x = 3 or x = +2 I mean

aargh 
Damon
x = 3 or x = +2

Precal 
Abi
I ended up with SS: (00,3]union [2,00)
why would it be 3 to 0? 
Precal 
Damon
because it is zero at 3
then when x approaches zero from the left it is like 6/.00000001 which is big positive 
Precal 
Damon
for example try x = 1
y = (1 + 1  6)/1
= 6/1
= +6 
Precal 
Damon
I can not seem to type anything right tonight
y = (1  1 6)/1
= 6/1
= +6 
ugh 
Abi
See, this is where i have trouble understanding.
if i put if in the calculator i see why it'd be 3 to 0
but in the exams the professor makes sure we are not able to graph inequality in calculator
my graph was off on paper, i just verified on ti84+ and it looks different :/ 
Precal 
Damon
LOL try 3/.001

Precal 
Damon
rather 6/.001

Precal 
Damon
No need for calculator
anything over anything is positive.
besides check when x = 1
which is between x = 3 and x = 0 
!? 
Abi
Aww it's not funny, it's frustating! :(
you want me to replace x with 3
not sure what you're meaning by that try 3/.001
where did you get the .001??
I'm so sorry i'm not understanding and thank you so much for helping 
Precal 
Damon
always check an easy point within the domain you are looking at.

Precal 
Damon
I am saying what will happen when x = .001 which is between x = 3 and x = 0
the answer you can see will be positive. 
Precal 
Damon
just about 6 / .001
which is positive 
Precal 
Damon
I have not used a calculator.

Precal 
Abi
yes, it gives me 6001.001 as an answer
You're not using a cal? 
Precal 
Abi
if i replace .001 with x i get 6001.001
how are you solving that without calculator 
Precal 
Abi
but if replace x with 4 i get a positive answer too!

Precal 
Damon
because if x = .001
then
x^2 is tiny
x is tiny
6 is 6
so we have 6/.001 which is 6000
which is pretty much what your calculator says 
Precal 
Abi
I'm still not understanding...
it's okay i'll keep trying to figure it out.
im clearly not double checking it right since i checked for 1 and got a positive answer but its supposed to be negative till 2 :/
thank you so much for your time!
it is honestly appreciated :) 
Precal 
Damon
if x = 4
(16 4 6) / 4
= 6/4
which is negative 
Precal 
Damon
If x = 1
then
(1 + 1  6)/1
= 4/1
= 4 
Precal 
Damon
You are welcome
Go back over all that and I bet you get it. 
Precal 
Abi
:D thank you!!!
I guess I've been staring at this for too long and probably not typing them correctly on the calculator!
THANK YOU SO MUCH!!!!!! 
Precal 
Damon
You are welcome, good luck with it. Forget the calculator and read that all carefully.
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