In solving a math problem (as well as other human life problems - but that is out of scope), it often makes sense to divide the problem into different cases, and then focus on each and every case to determine the outcome. Once you have determined the outcome of all possible cases, you can then sum up the outcomes from the different cases and that will be your solution to the problem. This problem solving technique is called casework. In using the casework technique, it is very important that you carefully analyze you problem to find a clear and structured way of dividing the problem into non-overlapping cases without gaps. We can use a math problem for example.

 

Find the solutions to equation ?2x+3?=3?x

 

We know that the number 2x+3 can be positive, 0, or negative. We can divide the above problem into 3 cases:

 

1.      When 2x+3 >0

2.      When 2x+3=0

3.      When 2x+3<0

 

In Case #1 & #2, the above equation will become 2x+3=3-x. Solving this linear equation, we have x = 0;

 

In Case #3, the above equation will become - (2x+3) = 3-x. Solving this equation, we have x = -6.

 

So to sum it all up, the solutions to above equation with an absolute expression is {-6, 0}.