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September 7th, 2011, 07:15 AM  #1 
Member Joined: Aug 2011 From: Alabama Posts: 93 Thanks: 0  Write inequality in the form a < x < b
A question asks me to write the inequality in the form a < x < b. How do I do this using the inequality x < 3 as an example? 
September 7th, 2011, 08:44 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,492 Thanks: 889 Math Focus: Elementary mathematics and beyond  Re: Write inequality in the form a < x < b
3 < x < 3.

September 7th, 2011, 10:42 AM  #3 
Member Joined: Aug 2011 From: Alabama Posts: 93 Thanks: 0  Re: Write inequality in the form a < x < b
Thank you for the reply, but you only solved the equation. Can you explain it?

September 7th, 2011, 12:57 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,492 Thanks: 889 Math Focus: Elementary mathematics and beyond  Re: Write inequality in the form a < x < b
x < 3 means x is within three units from zero, i.e. 3 < x < 3.

September 8th, 2011, 06:23 PM  #5 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: Write inequality in the form a < x < b
Remember that you have an absolute value of x. The "x < 3" part of it probably makes sense. The absolute value of a positive is just itself, so you can keep that "as is." But the absolute value of a negative number is the positive of that same number. So if you had 2, the absolute value is +2, which is less than 3, so that "fits." But the absolute value of 5 is +5, which is great than 3 so that doesn't work. Anything that is 3 or less, is going to be +3 or greater when you use the absolute value. So it also has to be greater than 3. Think of it like a mirror. 
September 8th, 2011, 08:06 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 461 Math Focus: Calculus/ODEs  Re: Write inequality in the form a < x < b
You can also use to write: Square both sides, since both are positive: We have two critical values: 3, 3 which creates 3 intervals: f(4) : ()() = + not part of solution. f(0) : (+)() =  part of solution : f(4) : (+)(+) = + not part of solution Thus, we find x is in the interval (3,3) which written as an inequality is: 3 < x < 3 

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