1.  The shortest answer is: because the absolute value function is defined differently in different parts of the number line.



2.  Slightly more extended answer is this:

    When we solve absolute value equation |ax + b| = c, for example, 
    we reduce it to solving TWO equations with linear functions.

    In each equation this linear function is determined in its own way.



3.  To get the most detailed explanations, see the lessons