# Precal

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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+x-6/x

I got SS: -infinity to -3 including -3 union -2 to infinity including -2

is that right?

• Precal -

EDIT WHERE INEQUALITY IS GREATER THAN OR EQUAL TO ZERO

• Precal -

do you mean
6/x
or do you mean
(x^2+x-6)/x
????

• Precal -

Sorry i should have put that in parenthesis
(x^2+x-6)/x greater than or equal to 0

• Precal -

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
(x-3)(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 -

(x+3)(x-2) = 0
x = -3 or x = +3
positive from x = -3 to x = 0
positive from x = +2 to x = +oo

• Precal -

Isn't it x^2+x-6 = 0
(x+3)(x-2) = 0?
x = -3 or x= +2?

• Precal -

x = 3 or x = +2 I mean

• aargh -

x = -3 or x = +2

• Precal -

I ended up with SS: (-00,-3]union [2,00)

why would it be -3 to 0?

• Precal -

because it is zero at -3
then when x approaches zero from the left it is like -6/-.00000001 which is big positive

• Precal -

for example try x = -1

y = (1 + 1 - 6)/-1
= -6/-1
= +6

• Precal -

I can not seem to type anything right tonight

y = (1 - 1 -6)/-1
= -6/-1
= +6

• ugh -

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 -

LOL try -3/-.001

• Precal -

rather -6/-.001

• Precal -

No need for calculator
-anything over -anything is positive.
besides check when x = -1
which is between x = -3 and x = 0

• !? -

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 -

always check an easy point within the domain you are looking at.

• Precal -

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 -

which is positive

• Precal -

I have not used a calculator.

• Precal -

yes, it gives me 6001.001 as an answer

You're not using a cal?

• Precal -

if i replace -.001 with x i get 6001.001

how are you solving that without calculator

• Precal -

but if replace x with -4 i get a positive answer too!

• Precal -

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 -

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 -

if x = -4
(16 -4 -6) / -4
= 6/-4
which is negative

• Precal -

If x = 1
then
(1 + 1 - 6)/1
= -4/1
= -4

• Precal -

You are welcome
Go back over all that and I bet you get it.

• Precal -

: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 -

You are welcome, good luck with it. Forget the calculator and read that all carefully.

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