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### 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/
```
Associated Topics:
High School Basic Algebra

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