How Do You Solve the Inequality |x+2/x+1| ≤ |x-3|?

AI Thread Summary
To solve the inequality |(x+2)/(x+1)| ≤ |x-3|, it is suggested to first solve the corresponding equation |(x+2)/(x+1)| = |x-3|. The discussion highlights that there are four combinations of positive and negative signs to consider, which are crucial for determining the solution intervals. Additionally, it is important to identify the values of x where the left side is not defined, as these points will help separate the regions for testing the inequality. The overall approach involves analyzing the critical points and testing intervals to find the solution set. Understanding these steps is essential for effectively solving the inequality.
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Homework Statement


|x+2/x+1|less than or equal to |x-3|
how do i solve this??
I couldn't find any way!
My lecturer did give me a hint saying that there are four combinations of + and -ve signs.

Homework Equations


The Attempt at a Solution

 
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With complicated inequalities it is usually best to solve the corresponding equation first. For what values of x is |(x+2)/(x+1)|= |x- 3|. For what values of x is that left side not defined? Those points separate ">" from "< ".
 

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