Algebra Foundations: Modulus, Inequalities, and Logarithms

To excel in advanced mathematics and competitive entrance exams, you must first master the core algebraic tools that appear in almost every complex problem. This text-based course is designed to take you from foundational definitions to confident problem-solving in modulus, inequalities, and logarithms. You will develop the mathematical maturity required for advanced engineering and science tracks by learning how to break down complex algebraic expressions step-by-step. By working through clear explanations and structured written proofs, you will build the analytical skills needed to solve non-routine mathematical problems with precision. What you'll learn: - Understand the formal definition of absolute value and solve complex modulus equations. - Master the rules of inequalities and apply interval notation to express solution sets. - Apply the method of intervals (wavy curve method) to solve polynomial and rational inequalities. - Learn the fundamental properties, laws, and change-of-base formula for logarithms. - Solve logarithmic equations and inequalities while respecting domain constraints. - Practice translating word problems into precise algebraic formulations. The course begins with foundational definitions of real numbers, absolute values, and basic interval notation. From there, you will progress through structured text lessons covering algebraic inequalities, the mechanics of logarithms, and systems of equations, concluding with integrated practice problems that combine all three core topics. This course is designed specifically for beginners, high school students, and aspirants of competitive STEM exams who want to solidify their mathematical foundations from the ground up. No advanced mathematical background is required to start. Begin reading today to build a bulletproof foundation in algebra.