Compound Inequality

Date: 9/15/96 at 16:30:48
From: Elizabeth Greenlee
Subject: Compound Inequality

     5x-1 > 4 and 6x+3 < 4x-1

  Individually, I can solve each inequality, but there is no 
intersection as far as I can see.  For 5x-1>4 I got x>1 and for 
6x+3<4x-1, I got x<-2.  How can a number be >1 and <-2 at the same 
time?  I may have worked the inequalities incorrectly, but I can't 
find the error there.  Here's what I did. Please tell me what I did 
wrong.

        5x-1>4      and       6x+3<4x-1
          5x>5                  6x<4x-4
           x>1                  2x<-4
                                 x<-2   Is there any intersection? 

Date: 9/18/96 at 0:51:2
From: Doctor Mike
Subject: Re: Compound Inequality

Hello Elizabeth,
  
Your analysis of this situation is right on the money. You did nothing 
wrong.  There is no x value to satisfy both inequalities.  
Congratulations.  
  
Sometimes a teacher or textbook will throw in a problem like this to 
make sure everybody's awake. Sometimes real life does the same thing.  
In cases where you find that there is no solution after you check your 
work, but you still are not sure, you could go back and verify that 
you have copied the problem down correctly. If one of the inequalities 
is reversed, then of course it's a completely different problem.
  
I hope this helps.

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/