Algebra — Linear Equations

About this lesson

This unit focuses on linear equations in one variable. It begins by introducing the concept of an equation and distinguishing linear equations from quadratic and cubic equations, as well as equations in two variables. Students learn to form linear equations from real-life situations, such as taxi fares, ticket prices, and geometric problems. The unit then covers solving equations using two methods: the substitution method (with a given substitution set) and the properties of equality (addition, subtraction, multiplication, and division). Examples and exercises involve finding solution sets within the sets of natural numbers, integers, and rational numbers. The unit also includes word problems, verification of solutions, and a variety of practice exercises, including multiple-choice questions, error analysis, and application problems in contexts like geometry, saving, sports, and employment. By the end, students should be able to form and solve linear equations in one variable, understand the relationship between substitution set and solution set, and apply these skills to real-life problems.