This research discusses the application of mathematics in economics, specifically in Real Number Systems and Inequalities, which play an important role in various fields such as science, engineering, and economics. The real number system includes rational and irrational numbers, which are used for continuous quantities. On the other hand, inequalities provide the foundation for analyzing mathematical relationships in various contexts. The objective of this study is to understand the properties of real numbers and their applications in solving everyday problems, as well as to explore the solutions to inequalities through graphical and analytical approaches. The methods used involve literature review and theory on practical cases, such as optimization and function modeling. The research findings indicate that the concepts of real numbers and inequalities can facilitate decision-making under certain conditions.