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Solving elementary algebra lies at the heart of this basic textbook. Some of the topics addressed include inequalities with rational functions, equations and inequalities with modules, exponential, irrational, and logarithmic equations and inequalities, and problems with trigonometric functions. Special attention is paid to methods for solving problems containing parameters. The book takes care to introduce topics with a description of the basic properties of the functions under study, as well as simple, typical tasks necessary for the initial study of the subject. Each topic concludes with problems for readers to solve, some of which may require serious effort and solutions are provided in all cases. Many of these problems were specifically created for this book and are set at university entrance exam or mathematical Olympiad level. The authors both have extensive experience in conducting and compiling tasks for exams and Olympiads. They seek to continue and share the traditions of Russian mathematical schools with schoolchildren, math teachers, and everyone who loves to solve problems.
Preface.
About the Authors.
Exponential and Logarithmic Equations and Inequalities.
Equations and Inequalities with Polynomials and Rational Functions.
Equations and Inequalities with Modulus.
Irrational Equations and Inequalities.
Trigonometric Equations and Inequalities.
Tasks for the Number of Solutions.
Problems That Reduce to the Study of a Quadratic Equation and the Selecting of Non-Negative Expressions.
Solving Problems Using a Geometric Image.
Inequalities.
Index