The proposed manual provides material for preparing for solving problems such as NW on the exam in mathematics, dedicated to inequalities and systems of inequalities. Numerous examples with detailed solutions and justifications show various methods and ideas for solving inequalities. For the convenience of using the book, reference materials and a brief theory are provided, and at the end of each paragraph - tasks for self-solution. The manual is intended for high school students, mathematics teachers, students of preparatory departments of universities, methodologists and tutors.