In this PowerPoint, we begin by recalling some of the most common algebraic techniques used to solve equations and inequalities. Then, we show that, for some cases, those methods won鈥檛 solve the problem, hence requiring for alternative techniques.
We then introduce the 鈥淪ign-change rule鈥� which can be used, either to prove the existence of a root of an equation in a given interval as to actually determine such root. Afterwards, we introduce the method of iterations, where we develop a full method to gradually obtain approximations to the root of a given equation.
In the last section, we explore different examples of worked exam-style questions, where all steps are clear and detailed.
Hopefully, this resource can help students in their preparation for examinations and can also be used as a complementary teaching tool, when delivering these topics.