Methods of teaching secondary school students to solve algebraic equations and inequalities and their systems

Relevance. The relevance of this study is conditioned by the integral role of algebraic equations and inequalities in mathematics education, as well as the need for effective methods and approaches to their teaching at the secondary school level. Purpose. The study aims to develop and appropriate methods for teaching secondary school students to solve algebraic equations and inequalities, including their systems, taking into account modern educational requirements and pedagogical approaches. Methodology. In the course of the study, methods such as experimental research, questionnaire surveys, and statistical analysis of data were used. Results. Because of the study, it was revealed that the innovative methodology for teaching the solution of algebraic equations and inequalities in secondary school had a positive impact on students' mastery of the material. The participants demonstrated a deeper understanding of algebraic concepts, increased independence in problem-solving, and developed critical thinking skills. They became more confident in analysing and interpreting problem conditions, identifying relationships between variables, and proposing adequate solutions. The new approach also improved students� motivation to study algebra and their academic performance, with increased interest and passion for the subject due to the interactive methods and practical tasks provided. Conclusions. The study confirms the effectiveness of the innovative methodology in the contemporary educational context of mainstream schools. The practical significance of the study lies in providing mainstream schoolteachers with tools to successfully teach students algebraic equations and inequalities, contributing to the development of analytical thinking and mathematical competence. Keywords: interactive lessons; visualization of mathematical concepts; individual progress; skill development