Question

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+x-6/x

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

is that right?

Answer 1

EDIT WHERE INEQUALITY IS GREATER THAN OR EQUAL TO ZERO

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

x = 3 or x = +2 I mean

Answer 8

x = -3 or x = +2

Answer 9

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

why would it be -3 to 0?

Answer 10

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

Answer 11

for example try x = -1

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

Answer 12

I can not seem to type anything right tonight

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

Answer 13

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 :-/

Answer 14

LOL try -3/-.001

Answer 15

rather -6/-.001

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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.

Answer 20

just about -6 / -.001
which is positive

Answer 21

I have not used a calculator.

Answer 22

yes, it gives me 6001.001 as an answer

You're not using a cal?

Answer 23

if i replace -.001 with x i get 6001.001

how are you solving that without calculator

Answer 24

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

Answer 25

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

Answer 26

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 :)

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

: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!!!!!!

Answer 31

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