How to solve this absolute value equation? Consider the absolute value equation:
|x| + |x-2| +|x-4|= 6
How to find the solution(s)?
My attempt:
For |x|, we got x, for x>=0 and -x, for x <0
For |x-2|, we got x-2, for x >= 0 and -(x-2), for x<0
For |x-4|, we got x-4, for x>=0 and -(x-4), for x<0
After this, I'm confused how to find the solutions? is it any easy way to find the solution?
Thanks

I think you misunderstand the absolute value. 
Note that $$|x|=\begin{cases}x &\text{if $x\ge 0$}\\-x &\text{if $x\lt 0$}\end{cases}$$
So, for example, 
$$|x-2|=\begin{cases}x-2 & \text{if $\color{red}{x-2}\ge 0$}\\-(x-2)& \text{if $\color{red}{x-2}\lt 0$}\end{cases}$$
So, for your question, separate it into four cases as
(1) $x\lt 0$.
(2) $0\le x\lt 2$.
(3) $2\le x\lt 4$.
(4) $x\ge 4$.
