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This is currently where I'm at. Can anyone explain how to do inequalities with absolute values on both sides?

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Do you know how to solve inequalities without absolute values?

 

If you have an equation with absolute values you can just look to all the possibilities, that means you eliminate the absolute values by limiting the variable to a certain set.

At the end you combine it all.

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it will be

 

1. remove the absolute "x+1<=x-3"

 

oh that's it. Absolute is meant to describe something cannot be negative like distance or price. Maybe more?

The absolute value is a function that describes the distance from 0.

 

You can remove it by choosing the right set for x:

x+1 <= -x + 3      for x in [-1,3] 

Here x+1 is positve and x-3 negative.

There are three different ones.

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