How does the number of solutions of the equation

$$
|x+2|-|2 x+8|=a
$$

depend on the value of the real parameter $a$?
Most people tried to solve the problem graphically. Those who did not receive full marks drew the graph of the function without any justification and then read off the final result from it.

The equation has no solution if $a>2$, one solution if $a=2$, and two solutions if $a<2$.