Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

xartaan Group Title

Got a question about a simple proof. Prove: If \[\frac{ x }{ x-1 } \le 2\] then x < 1 or x >= to 2. I approached this by multiplying both sides by (x-1), and factoring out x, which simplified to 2 <= x. I feel like this satisfies the hypothesis, but I feel like something is missing. I guess I just don't see how this is PROOF. Is it just that simple and I am missing the fundamental connection, or am I just way off base?

  • one year ago
  • one year ago

  • This Question is Closed
  1. Jemurray3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    You have to differentiate between the case where x<1 and x>1 when you multiply by x-1, because one case preserves the sign of the inequality and the other reverses it.

    • one year ago
  2. Jemurray3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    My proof would go something like: First, note that x cannot equal 1, as the expression is then undefined. Let us assume x >1. Then we may multiply both sides of the inequality by (x-1) which yields \[x \leq 2x-2 \] which can be simplified to \[x \geq 2\] On the other hand, lets assume x < 1. Then when we multiply we must reverse the sign of the inequality, yielding \[x \geq 2x-2 \] which simplifies to \[x \leq 1 \implies x<1 \text{ since }x\neq1\] Therefore, the condition \[\frac{x}{x-1} \leq 2 \implies x<1 \text{ or }x \geq 2\]

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

    Thanks a ton, I had a feeling something was missing!

    • one year ago
    • Attachments:

See more questions >>>

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.