Foundations of Algebraic Inequalities

Many students struggle to transition from solving equations to handling inequalities, often making critical sign errors or misinterpreting solution sets. This course provides a clear, step-by-step approach to mastering the core concepts of algebraic inequalities. By the end of this course, you will have a deep conceptual understanding of why inequalities behave the way they do and possess the necessary analytical skills to solve complex problems involving polynomials and absolute values. What you'll learn: * Understand the fundamental rules and properties governing algebraic inequalities and their manipulation. * Practice solving linear and compound inequalities using standard algebraic techniques. * Apply the sign chart method to efficiently solve quadratic and higher-degree polynomial inequalities. * Master the use of interval notation to accurately express solution sets on the number line. * Analyze and solve complex inequalities involving absolute values and rational expressions. The course begins with definitions and basic manipulation rules, progresses through methodical techniques for linear and quadratic forms, and concludes with advanced problem-solving strategies for handling polynomial and rational expressions. The material emphasizes conceptual clarity and detailed, written problem-solving practice. This course is designed for beginners, specifically high school or pre-university students, or anyone needing a strong, fundamental review of algebraic inequalities. No prior advanced mathematical knowledge is required, just basic algebra skills. Start building your rigorous mathematical foundation today.