# How can I generate an inequality based on its solution set?

Asked by zarnold (695) September 30th, 2007

I’m wondering if there’s some mathematical procedure for quickly finding an inequality based on its solution set. Thanks

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I don’t think theres any defined algorithm for finding an inequality. Generally when I’ve needed to do something like this, I know/recognize the pattern of the solution set, to the point where I can generate a valid inequality. Maybe an example would help?

Perchik (4982)

I agree with Perchik… specific details would make this easier to answer. What is your solution set?

finkelitis (1907)

i have to create an inequality of the form abs(x-c)<y; i have the solution set (0.4).

zarnold (695)

I’m assuming you mean that x can take any value between 0 and 4 exclusive with this notation…

To get this, the best thing to do is to notice that abs(x-c) is really a 1-dim circle (i.e., a line segment) with it’s center at c (thus the choice of letter). Using absolute value makes more sense in higher dimensions, where you actually get circles and spheres when you’re trying to do this kind of thing. So you can think about this as being the question:

“You have the line segment (0,4); what is its center c and its ‘radius’ y?”, where radius means the distance from the center to the outside.

If that makes sense to you, I think that’s the easiest way to do it (and this kind of geometric thinking is really the origin of worrying about absolute values at all). If this method is not helpful for you, I can suggest other approaches.

finkelitis (1907)

thanks much!

zarnold (695)

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