A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Got a question about a simple proof.
Prove: If \[\frac{ x }{ x1 } \le 2\] then x < 1 or x >= to 2.
I approached this by multiplying both sides by (x1), 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?
 2 years ago
Got a question about a simple proof. Prove: If \[\frac{ x }{ x1 } \le 2\] then x < 1 or x >= to 2. I approached this by multiplying both sides by (x1), 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?

This Question is Closed

Jemurray3
 2 years ago
Best ResponseYou've already chosen the best response.2You have to differentiate between the case where x<1 and x>1 when you multiply by x1, because one case preserves the sign of the inequality and the other reverses it.

Jemurray3
 2 years ago
Best ResponseYou've already chosen the best response.2My 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 (x1) which yields \[x \leq 2x2 \] 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 \[x \geq 2x2 \] which simplifies to \[x \leq 1 \implies x<1 \text{ since }x\neq1\] Therefore, the condition \[\frac{x}{x1} \leq 2 \implies x<1 \text{ or }x \geq 2\]

xartaan
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks a ton, I had a feeling something was missing!
Ask your own question
Ask a QuestionFind 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
 Engagement 19 Mad Hatter
 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.