April 7th, 2014, 11:50 AM  #1 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  find solve
solve 1/2(x1) 4/x +15/2(x+1)>=1

April 7th, 2014, 11:53 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 
You have recently posted a slew of questions, but no effort is shown in any of them. We aren't really helping you by doing your homework for you...it would be better if you showed your attempts and thoughts so we can guide you rather than hand out answers. 
April 7th, 2014, 10:29 PM  #3 
Senior Member Joined: Mar 2014 Posts: 112 Thanks: 8 
I got 1 < x ≤ 2 or (1, 2]. Here's why. At x = 1 the expression is undefined. Hence 1 < x. Multiply both sides by 2x(x + 1)(x  1) and we get 0 ≥ (x  2)(x²  2x + 2). Since x²  2x + 2 > 0 for all x i.e. the discriminant, x  2 ≤ 0 i.e. x ≤ 2. I think there's a bit more solutions that I've posted. I'll let others reply. Last edited by the john; April 7th, 2014 at 10:33 PM. 
April 8th, 2014, 01:38 AM  #4 
Senior Member Joined: Mar 2014 Posts: 112 Thanks: 8 
1 < x < 0 or (1, 0)

April 8th, 2014, 02:06 AM  #5 
Senior Member Joined: Mar 2014 Posts: 112 Thanks: 8 
I solved for $\displaystyle \frac{1}{2(x\,\,1)}\,\,\frac{4}{x}\,+\,\frac{15}{2(x\,+\,1)}\,\geq\,1 \text{.}$


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