Hi All,
Just trying to solve:
(2x+1)/(2x-1)>=1
I try:
2x+1>=2x-1
0>=-2 (not the answer I want)
I tried:
(2x+1)(2x-1)/(2x-1)(2x-1)>=1
4x^2-1>=4x^2-4x+1
-2>=-4x
x>=1/2 (can't be this, it is undefined)
I also tried:
(2x+1)(2x+1)/(2x-1)(2x+1)>=1
4x^2+4x+1>=4x^2-1
4x+1>=-1
4x>=-2
x>=-1/2 (but this answer doesnt work with the inequality...0>=1??)
Not sure what to do now...by looking at the graph I think x>=1/2...but like i said, this is undefined...
This is the strangest thing...
But, any way, sometimes intuition proves to be invaluable.
Hint:
If both the numerator and the denominator are greater than zero, then the given quotient will be greater than one.
If both the numerator and the denominator are less than 0, then the given quotient will be less than one.
If both the numerator and the denominator are zero, then the given quotient is undefined.
You were on to something when you were thinking about x=1/2. Look at that again...
Thanks for the help guys. I appreciate it!
To Mr. Fantastic....this is a question for a maths test (well, its a test to test my maths knowledge to be a maths teacher), and Im sure the answer is something more than looking at the graph (which I have done, and see the answer) I just need to show it mathematically.
To VonNemo19....I sort of understand what you are saying...but not sure how it helps me...
I'm wondering if I should take a limit from the right hand side? ie
lim x-->1/2+ of (2x+1)/(2x-1)
to show that it is greater than 1?