Abstract
The article discusses the ways of developing skills and abilities to effectively solve problems when describing methods for solving equations and inequalities, clarifying theoretical knowledge, the basics of forming skills for practical application. The formation of mathematical concepts through solving problems in teaching mathematics opens the way to the development of mathematical thinking, the application of knowledge in practice, and the development of search skills. To master a mathematical concept, along with its definition, it is necessary to know its features and properties. This can be achieved primarily through problem solving and exercise. Problem solving is based on the development of new methods, the creation of algorithms, ways of developing practical skills in the methods and techniques mastered with the help of tasks.In addition, transforming equations and inequalities through the development of thinking skills helps to identify common or special properties in order to draw correct conclusions. Solving various problems, it shows what operations should be used to determine the situation in which a solution was found, and what features of the solution allow choosing the most effective methods. Thanks to the theoretical substantiation of the general article, it is possible to master convenient methods for solving equations and inequalities of various structures.