Posted by Abi on Saturday, June 22, 2013 at 7:08pm.
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, Saturday, June 22, 2013 at 7:08pm
EDIT WHERE INEQUALITY IS GREATER THAN OR EQUAL TO ZERO

Precal  Damon, Saturday, June 22, 2013 at 7:10pm
do you mean
6/x
or do you mean
(x^2+x6)/x
???? 
Precal  Abi, Saturday, June 22, 2013 at 7:17pm
Sorry i should have put that in parenthesis
(x^2+x6)/x greater than or equal to 0 
Precal  Damon, Saturday, June 22, 2013 at 7:37pm
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, Saturday, June 22, 2013 at 7:41pm
(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, Saturday, June 22, 2013 at 7:41pm
Isn't it x^2+x6 = 0
(x+3)(x2) = 0?
x = 3 or x= +2? 
Precal  Damon, Saturday, June 22, 2013 at 7:41pm
x = 3 or x = +2 I mean

aargh  Damon, Saturday, June 22, 2013 at 7:42pm
x = 3 or x = +2

Precal  Abi, Saturday, June 22, 2013 at 7:43pm
I ended up with SS: (00,3]union [2,00)
why would it be 3 to 0? 
Precal  Damon, Saturday, June 22, 2013 at 7:45pm
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, Saturday, June 22, 2013 at 7:46pm
for example try x = 1
y = (1 + 1  6)/1
= 6/1
= +6 
Precal  Damon, Saturday, June 22, 2013 at 7:48pm
I can not seem to type anything right tonight
y = (1  1 6)/1
= 6/1
= +6 
ugh  Abi, Saturday, June 22, 2013 at 7:49pm
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, Saturday, June 22, 2013 at 7:51pm
LOL try 3/.001

Precal  Damon, Saturday, June 22, 2013 at 7:53pm
rather 6/.001

Precal  Damon, Saturday, June 22, 2013 at 7:55pm
No need for calculator
anything over anything is positive.
besides check when x = 1
which is between x = 3 and x = 0 
!?  Abi, Saturday, June 22, 2013 at 7:56pm
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, Saturday, June 22, 2013 at 7:56pm
always check an easy point within the domain you are looking at.

Precal  Damon, Saturday, June 22, 2013 at 7:57pm
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, Saturday, June 22, 2013 at 7:58pm
just about 6 / .001
which is positive 
Precal  Damon, Saturday, June 22, 2013 at 7:58pm
I have not used a calculator.

Precal  Abi, Saturday, June 22, 2013 at 7:59pm
yes, it gives me 6001.001 as an answer
You're not using a cal? 
Precal  Abi, Saturday, June 22, 2013 at 8:00pm
if i replace .001 with x i get 6001.001
how are you solving that without calculator 
Precal  Abi, Saturday, June 22, 2013 at 8:02pm
but if replace x with 4 i get a positive answer too!

Precal  Damon, Saturday, June 22, 2013 at 8:06pm
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, Saturday, June 22, 2013 at 8:08pm
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, Saturday, June 22, 2013 at 8:08pm
if x = 4
(16 4 6) / 4
= 6/4
which is negative 
Precal  Damon, Saturday, June 22, 2013 at 8:10pm
If x = 1
then
(1 + 1  6)/1
= 4/1
= 4 
Precal  Damon, Saturday, June 22, 2013 at 8:12pm
You are welcome
Go back over all that and I bet you get it. 
Precal  Abi, Saturday, June 22, 2013 at 8:14pm
: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, Saturday, June 22, 2013 at 8:20pm
You are welcome, good luck with it. Forget the calculator and read that all carefully.