Simple Mathematical Models: Equations and Inequalities

This module introduces the fundamental concepts of equations with one unknown variable, exploring their domains and solution sets. Students will learn algorithms for solving linear equations and develop skills in isolating variables within literal equations (formulas). The module establishes a strong foundation for understanding algebraic problem-solving techniques.

This module focuses on quadratic equations and their various solution methods. Students will learn multiple approaches including factoring, completing the square, and applying the quadratic formula. The module also covers techniques for solving equations that can be reduced to quadratic form, providing essential tools for more complex algebraic problems.

This module presents different algorithms for solving systems of two linear equations with two unknowns. Students will learn various solution methods while gaining insight into the geometric interpretation of these systems. The module bridges basic equation solving with more advanced mathematical concepts needed for practical applications.

This module reviews the fundamental properties of inequalities and applies them to solve various types of inequalities, including linear, quadratic, and rational forms. Students will learn how inequality solutions differ from equation solutions and develop techniques for representing and analyzing these mathematical relationships.

This culminating module consolidates all concepts from the course through practical problem-solving. Students will learn to translate real-world scenarios into mathematical models using equations and inequalities, emphasizing the crucial connection between semantic understanding and algebraic syntax. This module bridges theoretical knowledge with practical applications.