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

[benleong2008]

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

 

[HallsofIvy]

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 "< ".