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Absolute value problems are a cornerstone of algebra, often presenting a challenge in standardized tests due to the need for careful case analysis. This course provides a systematic, rigorous approach to understanding and solving these critical mathematical structures. Upon completing this course, you will gain a deep, systematic understanding of absolute value functions, allowing you to confidently solve both equations and inequalities and prepare for higher-level mathematics. What you'll learn: * Understand the formal definition of absolute value and its geometric meaning on the number line. * Master the systematic algebraic methods for solving single and double absolute value equations. * Apply rigorous case analysis and interval testing to determine the solution sets for inequalities. * Learn how to interpret and configure piecewise functions derived from complex absolute value expressions. * Practice translating word problems into absolute value expressions and solving them efficiently for maximum accuracy. This text-only course begins with foundational concepts and definitions, progresses through step-by-step algebraic methods, and culminates in complex, multi-variable problem-solving exercises typical of rigorous entrance exams. This course is designed for beginners, including high school students and anyone preparing for college-level mathematics placement or entrance exams. No prior advanced knowledge is required. Start reading today to solidify your mathematical foundations.