5  0  5  
5  0  
0  5  
10  0  0  0 
In the following examples, we develop the algebraic solution process; the reader can have some help from the drawing of the appropriate graphs. The reader who is not familiar graphs can skip to chapter 2 subsection graph of a function and return to the present section afterwards.
Let us draw a table, in order to write the different expressions without an absolute value:
the equation  
solutions  none  none 
Look at Figure 2: the equation's left side corresponds to the blue graph, the right side corresponds to the red graph. The solution of the equation is the coordinate of the unique point of intersection of these graphs.
We draw a table:
the inequation  

Finally the solution set of the given inequation is .
Look at Figure 3: the inequation's left side corresponds to the blue graph, the right side corresponds to the red graph. The solution set of the inequation is the set of coordinates for which the blue graph is higher than the red one.
We draw a table:
the inequation  

Now look at Figure 4: the inequation's left side corresponds to the blue graph, the right side corresponds to the red graph. The solution set is the set of coordinates for which the blue graph is higher than the red one.
Noah DanaPicard 20071228