Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

sinusoidal

  • one year ago

2|x-1| < x^2 answers are: x < -1 - sqrt(3) or x > -1+sqrt(3) I'm having trouble coming up with these solutions. Could someone help me with the steps?

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

    Did you try looking at 2|x-1|=x^2 first When we have |f(x)|=a, we try to solve this by doing f(x)=-a of f(x)=a Now keep in mind that a needs to be positive or 0. Guess what? x^2 is a positive number or 0.

  2. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm tell you to solve the following 2(x-1)=x^2 or 2(x-1)=-x^2

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

    I've got it now. I thought that I tried that before, but I think I was just making so many mistakes that I became too sloppy and frustrated

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

    thanks

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

    getting rid of the inequalities made it a lot simpler.

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

    how would you know how to replace the inequalities back into the answer?

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

    analytically, I mean

  8. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    One of the equations you solve, you will get a complex answer. The other equation you solve, will give you two real solutions. You should see x=-1+sqrt(3) or x=-1-sqrt(3). You can test intervals to see where we have 2|x-1|<x^2 |dw:1380904061968:dw|

  9. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1380904086865:dw| 2|-10-1|<10^2 True/False 2|0-1|<0^2 True/False 2|10-1|<10^2 True/False

  10. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The inequalities that come back true are the intervals you want to include in your solution.

  11. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The first inequality, I went ahead and said 10^2 instead of (-10)^2 since 10^2 is the same result at (-10)^2.

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

    right, I get it now. I wasn't thinking about getting rid of the inequalities and just replacing them back at the end. it makes the process a lot simpler

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

    and I was thrown off by the complex solution too

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

    thanks

  15. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Np. Have fun. :)

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.