"Methodology for Solving Non-Standard Equations and Inequalities"

This article examines methodological approaches to solving non-standard equations and inequalities in modern mathematics education. Non-standard equations and inequalities differ from traditional algebraic problems because they require creative reasoning, transformation techniques, logical analysis, and the application of advanced mathematical methods. The study highlights the importance of heuristic strategies, substitution methods, graphical interpretations, functional analysis, and inequality transformations in solving unconventional mathematical problems. The article also discusses pedagogical approaches for developing students’ analytical thinking and problem-solving competence. Through theoretical analysis and practical examples, the research demonstrates that systematic methodologies improve mathematical reasoning skills and foster deeper conceptual understanding.