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Precal

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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?

  • 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 -

    just about -6 / -.001
    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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