X greater than 25, OR less than 30

Date: 8/17/96 at 19:13:15
From: Anonymous
Subject: "Or" Two Inequalities

x > 25  or  x < 30

I think the set of answers is {26,27,28,29} but the "or" part in the 
problem is bugging me.  Is my answer correct or is there a different 
way to do it?  

 Thank you for your help. 

Date: 8/30/96 at 16:49:34
From: Doctor James
Subject: Re: "Or" Two Inequalities

You are quite right to have the "or" part bug you. Let's look at the
problem a bit.

There are three parts of the number line that we have to be concerned 
with. The first part is all n<=25, the second is all n such that 
25 < n < 30, and the last part is all n>=30. So, we can just look at 
one number in each part, and see if it satisfies the equation.

First, let's take 20 (which is in part one).  Is it either greater 
than 25 _or_ less than 30? Well, 20 certainly isn't greater than 25, 
but it _is_ less than thirty. So, it is either greater than 25 or less 
than 30.

Now let's look at 28 (part 2). Is it either greater than 25 or less
than 30?  Well, it is greater than 25, and it is also less than 30! So
it is definately either greater than 25 or less than 30.

Finally, let's look at 35. Is it either greater than 25 or less than
30? Well, it's greater than 25, but it's not less than thirty. But, 
since it is greater than 25, it still is either greater than 25 or 
less than 30.

So, the answer is all three sections, which is in fact all of the 
number line! So the answer is all real numbers.

A quick summary is that if you connect two statements with an "and", 
both sides of the statement must be true. If you connect two 
statements with an "or", only one side must be true.

I hope you get this in time!

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