A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

steve816

  • one year ago

Please help me solve the inequality!

  • This Question is Closed
  1. steve816
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[x^3-x^2-72x >0\]

  2. steve816
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I solved for x and got x = 0, 9, -8 Not sure what to do from there.

  3. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so you solved x^3 - x^2 - 72x = 0 for x and you got x = 0, x = 9, x = -8 ??

  4. steve816
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes

  5. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ok first draw a number line and plot those three values on it |dw:1440998491371:dw|

  6. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1440998528778:dw|

  7. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    label the different regions A,B,C,D |dw:1440998552769:dw|

  8. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1440998579792:dw|

  9. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1440998592421:dw|

  10. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1440998604341:dw|

  11. steve816
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay

  12. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    x^3 - x^2 - 72x factors to x(x-9)(x+8) then set up a sign chart where the factors are written in a column on the left side the regions are written along the top row like this |dw:1440998659579:dw|

  13. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    now let's pick a number from region A this could be any number you want as long as it's less than -8. So let's pick -9 if x = -9, then the sign of x is negative. We put a negative sign/symbol in the first row, first column like this |dw:1440998809112:dw|

  14. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    keep x = -9 the same what is the value of x-9? that is x-9 = -9-9 = -18 which is also negative so place a negative symbol in the "A" column and "x-9" row |dw:1440998838462:dw|

  15. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    if x = -9, then x+8 = -9+8 = -1 which is also negative |dw:1440998879510:dw|

  16. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I'm going to let y = x^3 - x^2 - 72x and write "y" in the bottom of the left most column |dw:1440998908837:dw|

  17. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    to find the sign of y for column A (is y positive or negative?) we multiply the signs in column A negative*negative*negative = positive*negative = negative so ultimately, y is negative when x < -8, ie in region A |dw:1440998977212:dw|

  18. steve816
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So I did all the work and got x <- 8 -8 < x < 0 x > 9 Is this right?

  19. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    does the sign chart make sense? if so, then go ahead and fill out the rest of it so I can see what you got

  20. steve816
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I figured out how to use the chart and made sense to me. So I got the answers that I wrote above.

  21. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you should have this sign chart |dw:1441000190738:dw|

  22. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    take a few moments to check what I got to make sure you got the same things

  23. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    did you get the same table?

  24. steve816
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yup!

  25. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    ok great, just checking

  26. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    notice how we want to solve for x in `x^3 - x^2 - 72x > 0` which is the same as `y > 0` since I made `y=x^3 - x^2 - 72x`

  27. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    look in the chart when y > 0 ie when there's a + sign in the y row |dw:1441001180490:dw|

  28. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    that corresponds to the intervals `-8 < x < 0` and `x > 9` |dw:1441001210042:dw|

  29. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so the solution to `x^3 - x^2 - 72x > 0` is `-8 < x < 0` OR `x > 9` we write \[\Large (-8, 0) \cup (9, \infty)\] if we wanted to state the entire solution set in interval notation the graph confirms all this https://www.desmos.com/calculator/6qe6nf0jao

  30. steve816
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Wow just wow *clap clap clap* Absolutely brilliant! Thanks for your time and help man, really appreciate it.

  31. jim_thompson5910
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    I'm glad it's all clicking now

  32. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.