ABSTRACT
Despite the existence of substantial literature on algebraic inequalities and a significant number of solved examples, there is a clear absence of systematic exposition of the techniques through which an algebraic inequality can be proved. Consequently, this chapter covers various techniques for proving algebraic inequalities. Despite that some of the techniques for proving inequalities have been covered well in the available literature, there are also a number of powerful methods and techniques for proving algebraic inequalities which did not receive adequate coverage. Therefore, this chapter compiled existing and introduced new methods for proving algebraic inequalities. A good awareness of the available tools through which an inequality can be proved reduces the dependence on inspiration and clever tricks in proving algebraic inequalities, which enhances the power of researchers and practitioners in using inequalities to improve reliability and reduce uncertainty and risk.
