A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Helpjebal

  • one year ago

This is a sample question from my lesson. f(x) = √(20 - 2x) the lesson says the answer is x ≤ 10. In my textbook it says "the expression under a radical may not be negative." So, how do I change the sign and solve to get the answer above?

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

    You know that you can NOT take the square root of a NEGATIVE. Correct?

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

    yes, i know

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

    Ok, so therefore the part inside the square root (the 20-2x), must be greater than or equal to 0. i.e: \(20-2x\ge0\)

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

    \(\color{blue}{1)}\) Add \(2x\) to both sides. \(\color{blue}{2)}\) Divide by \(2\) on both sides.

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

    Oh I see! So the addition would take away the negative sign leaving us to solve for x as normal? and adding on the other side wouldn't change ≥ to ≤? like 20 - 2x ≥ 0 20 ≤ 2x 20/2 ≤ 2x/2 10 ≤ x?

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

    incorrect

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

    Follow me carefully. \(\large\color{black}{ \displaystyle 20-2x\ge0 \\[0.5em]}\) \(\large\color{black}{ \displaystyle 20-2x \color{blue}{+2x}\ge0\color{blue}{+2x} \\[0.5em]}\) The \(-2x\) and \(+2x\) will cancel each other out. \(\large\color{black}{ \displaystyle 20\ge2x \\[0.5em]}\) Divide both sides by 2 \(\large\color{black}{ \displaystyle 10\ge x \\[0.5em]}\)

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

    So, the 10 is greater than (or equal to) x. ` (Not the other way around) `

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

    oh i see! i get it now! thank you so much!

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

    Ok, very nice.

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

    You can logically check that x is NOT greater than 10, because if you choose for example x=11, then you get: 20-2(11) 20-22 -2 and thus, since the part inside the square root can NOT be negative,, you can tell that x is NOT greater than 10.

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

    And you can logically see why x=10, or other x values that are smaller than 10 make the square root 0 or greater than 0 (which is perfectly valid for us).

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

    i never knew to check it like that. That's very good to know! thanks :)

  14. 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.