Q:

What's the meaning of an inequation with absolute value and how to solve that? 

I was doing an exercise and I found that for example:
| x - 2/3|= 2
x is 8/3 or -4/2 because x less 2/3 needs to be 2 or -2 because the distance between 2 or -2 to 0 is the same (2). 
But when applying this to an inequation I don't understand the meaning.  For example:
|x| < 3 
How can I solve that?  
I would appreciate if someone could help me understanding that. 

A:

$$\left| x-\frac { 2 }{ 3 }  \right| =2\quad \Rightarrow \begin{cases} x-\frac { 2 }{ 3 } =2 \\ x-\frac { 2 }{ 3 } =-2 \end{cases}\Rightarrow \begin{cases} x=\frac { 8 }{ 3 }  \\ x=-\frac { 4 }{ 3 }  \end{cases}\\ \left| x \right| <3\Rightarrow \quad -3<x<3$$

