Abstract:

Although inequalities that naturally arise in applications often involve functions that are not linear or quadratic, many high school graduates come to college with a rather limited knowledge in this area. Typically, they will be able to solve linear inequalities; however, these students will have difficulties even with simple quadratic inequalities. On the other hand, many of them will be able to solve relatively complex equations. The reason for this phenomenon is clear: the traditional methods of solving non-linear inequalities significantly differ from that of the corresponding equations.

In order to be able to solve inequalities that are not linear or quadratic, one needs to learn some specific techniques. There are a number of relevant techniques of solving inequalities such as the traditional, “case by case”, method or the graphing method.

The purpose of this presentation is to provide an insight into a method that we call the Interval Method of solving inequalities. We show that the difference between solving inequalities and corresponding equations practically disappears if one chooses to use this method.

We do not claim that the Interval Method is new because it is based on a simple observation, and we believe that many instructors use it in one form or another. Our goal is to present this method clearly and systematically and provide a number of examples to outline its possible applications. We also compare the Interval Method with other methods of solving inequalities.