# Math Help - Finding all r ∈ R such that r<1+1/r?

1. ## Finding all r ∈ R such that r<1+1/r?

Find all r ∈ R such that r<1+1/r?
So I'm having difficulty with this problem.
I've figured out that r is a variable and r does not = 0 and by solving it, multiplying both sides by r is incorrect.

Can you guys help me with this problem?
My first instinct is to just multiply both sides by r but that's apparently wrong.

Any help is appreciated.

I got some help elsewhere. Thanks though.

2. ## Re: Finding all r ∈ R such that r<1+1/r?

Originally Posted by paperclip5
Find all r ∈ R such that r<1+1/r?
So I'm having difficulty with this problem.
I've figured out that r is a variable and r does not = 0 and by solving it, multiplying both sides by r is incorrect.

Can you guys help me with this problem?
My first instinct is to just multiply both sides by r but that's apparently wrong.

Any help is appreciated.

I got some help elsewhere. Thanks though.
It's not that multiplying both sides by r is wrong- you just have to be careful. If you multiply both sides of an inequality by a negative number, you reverse the direction of the inequality.

Yes, as you say, r cannot be 0- so it is either positive or negative. If it is positive, multiplying both sides by r gives $r^2< r+ 1$ which is the same as $r^2- r- 1< 0$. If r is negative, multiplying both sides by r gives $r^2> r+ 1$ which is the same as $r^2- r- 1> 0$. Obviously, determining where $r^2- r- 1= 0$ is important in solving those! Don't forget that the first is only true for r> 0 and the second for r< 0.