Friday

February 12, 2016
Posted by **Abi** on Saturday, June 22, 2013 at 7:08pm.

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 -
**Abi**, Saturday, June 22, 2013 at 7:08pmEDIT WHERE INEQUALITY IS GREATER THAN OR EQUAL TO ZERO

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**Damon**, Saturday, June 22, 2013 at 7:10pmdo you mean

6/x

or do you mean

(x^2+x-6)/x

????

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**Abi**, Saturday, June 22, 2013 at 7:17pmSorry i should have put that in parenthesis

(x^2+x-6)/x greater than or equal to 0

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**Damon**, Saturday, June 22, 2013 at 7:37pmwell 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 -
**Damon**, Saturday, June 22, 2013 at 7:41pm(x+3)(x-2) = 0

x = -3 or x = +3

positive from x = -3 to x = 0

positive from x = +2 to x = +oo

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**Abi**, Saturday, June 22, 2013 at 7:41pmIsn't it x^2+x-6 = 0

(x+3)(x-2) = 0?

x = -3 or x= +2?

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**Damon**, Saturday, June 22, 2013 at 7:41pmx = 3 or x = +2 I mean

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

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**Abi**, Saturday, June 22, 2013 at 7:43pmI ended up with SS: (-00,-3]union [2,00)

why would it be -3 to 0?

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**Damon**, Saturday, June 22, 2013 at 7:45pmbecause it is zero at -3

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

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**Damon**, Saturday, June 22, 2013 at 7:46pmfor example try x = -1

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

= -6/-1

= +6

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**Damon**, Saturday, June 22, 2013 at 7:48pmI can not seem to type anything right tonight

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

= -6/-1

= +6

- ugh -
**Abi**, Saturday, June 22, 2013 at 7:49pmSee, 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 :-/

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**Damon**, Saturday, June 22, 2013 at 7:51pmLOL try -3/-.001

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**Damon**, Saturday, June 22, 2013 at 7:53pmrather -6/-.001

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**Damon**, Saturday, June 22, 2013 at 7:55pmNo 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 7:56pmAww 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

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**Damon**, Saturday, June 22, 2013 at 7:56pmalways check an easy point within the domain you are looking at.

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**Damon**, Saturday, June 22, 2013 at 7:57pmI am saying what will happen when x = -.001 which is between x = -3 and x = 0

the answer you can see will be positive.

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**Damon**, Saturday, June 22, 2013 at 7:58pmjust about -6 / -.001

which is positive

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**Damon**, Saturday, June 22, 2013 at 7:58pmI have not used a calculator.

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**Abi**, Saturday, June 22, 2013 at 7:59pmyes, it gives me 6001.001 as an answer

You're not using a cal?

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**Abi**, Saturday, June 22, 2013 at 8:00pmif i replace -.001 with x i get 6001.001

how are you solving that without calculator

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**Abi**, Saturday, June 22, 2013 at 8:02pmbut if replace x with -4 i get a positive answer too!

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**Damon**, Saturday, June 22, 2013 at 8:06pmbecause 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

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**Abi**, Saturday, June 22, 2013 at 8:08pmI'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 :)

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**Damon**, Saturday, June 22, 2013 at 8:08pmif x = -4

(16 -4 -6) / -4

= 6/-4

which is negative

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**Damon**, Saturday, June 22, 2013 at 8:10pmIf x = 1

then

(1 + 1 - 6)/1

= -4/1

= -4

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**Damon**, Saturday, June 22, 2013 at 8:12pmYou are welcome

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

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**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!!!!!!

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**Damon**, Saturday, June 22, 2013 at 8:20pmYou are welcome, good luck with it. Forget the calculator and read that all carefully.