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/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.