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September 11th, 2009, 04:39 AM  #1 
Newbie Joined: Sep 2009 Posts: 4 Thanks: 0  solving (2x+1)/(2x1)>=1
Hi All, Just trying to solve: (2x+1)/(2x1)>=1 I try: 2x+1>=2x1 0>=2 (not the answer I want) I tried: (2x+1)(2x1)/(2x1)(2x1)>=1 4x^21>=4x^24x+1 2>=4x x>=1/2 (can't be this, it is undefined) I also tried: (2x+1)(2x+1)/(2x1)(2x+1)>=1 4x^2+4x+1>=4x^21 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... 
September 11th, 2009, 03:58 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,762 Thanks: 697  Re: solving (2x+1)/(2x1)>=1
You have to consider 2 cases separately x>1/2 and x<1/2. When multiplying by 2x1 you will get 1 > 1 in the first case (true) and 1 < 1 in the second case (false). So the answer you are expecting x > 1/2 is correct.

September 12th, 2009, 04:01 PM  #3 
Newbie Joined: Sep 2009 Posts: 4 Thanks: 0  Re: solving (2x+1)/(2x1)>=1
is that really the answer, even though it is undefined at x=1/2

September 13th, 2009, 03:24 AM  #4  
Senior Member Joined: Mar 2009 Posts: 318 Thanks: 0  Quote:
Why? Because you do not know what the sign on the denominator is (it's a variable expression!), so you can't know whether or not to flip the inequality sign! Instead, move everything over to one side of the inequality: Convert to a common denominator: Now find the xvalues which make for zeroes of the numerator and undefined values for the denominator, use these xvalues to split up the number line, and then find the intervals on which the rational expression is positive....  
September 13th, 2009, 06:28 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,652 Thanks: 2085 
Clearly, 2/(2x  1) ? 0 ? (2x  1)/2 > 0 (since equality isn't possible in the leftmost inequality), i.e., x  1/2 > 0, i.e., x > 1/2. 

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