Remarks on solutions of equations with absolute value function

In this paper, we give the proposition of didactic discussion on the existence of solutions of some equations containing expressions with absolute value. We are interested in the possibility of applying the method of conceptual problem solving. Under this term we understand such a procedure, in which the solver is not limited to the automatic application of the definition of the absolute value, but he can reject some cases based on his mathematical knowledge. To do this, one must make use from various features of this concept - not only from its definition.