1.1 Linear Equations and Solutions

Solve and interpret linear equations in one variable using algebraic techniques.

本节包含的知识点

• 1.1.1 Linear Equation Definition and Standard Form — Understand the definition of linear equations in one variable and express them in standard form ax + b = 0.
• 1.1.2 Solving Linear Equations Using Inverse Operations — Apply inverse operations (addition, subtraction, multiplication, division) to isolate the variable and solve for x.
• 1.1.3 Multi-Step Equation Solving — Solve linear equations requiring multiple operations, including combining like terms and distributing coefficients.
• 1.1.4 Equations with Variables on Both Sides — Solve linear equations where the variable appears on both sides by collecting variables on one side.
• 1.1.5 Solution Verification and Interpretation — Verify solutions by substitution and interpret the meaning of solutions in context.
• 1.1.6 Special Cases: Identity and No Solution — Identify and interpret equations with infinite solutions (identities) and equations with no solution (contradictions).