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Solve the inequality |x - 2|/|x + 3| < 7.

May 23, 2020

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$$\frac{|x-2|}{|x+3|}<7$$

1) For starters x cannot equal -3.  Why is that?

2)  If x=2 then is it true?  Why?

3)  So I need to look at 3 regions.  Where x is less than -3, where x is between -3 and 2, and lastly where x is bigger than 2.

When x<-3,

x-2 is negative and x+3 is also neg so this means

|x-2| = -(x-2)=2-x

|x+3|=-(x+3)| = -x-3

See if you can continue from here.

If you get stuck then, display what you have done, and I will help further.

Please no one do any more unless the asker displays a concerted effort first.

\frac{|x-2|}{|x+3|}<7

May 23, 2020
edited by Melody  May 23, 2020