Solving Linear Equations
Grade 6 Mathematics — Algebra
🎯 Learning Goal: By the end of this lesson, you will be able to solve linear equations step-by-step, from simple one-step problems to more complex multi-step equations!
📐 1. What is a Linear Equation?
Definition:
A linear equation is an equation where the variable (usually x) has a power of 1. This means we only see x, never x², x³, or higher powers.
Standard Forms:
- ax + b = c — variable on one side
- ax + b = cx + d — variables on both sides
Examples of Linear Equations:
✅ 2x + 5 = 11
✅ 3x − 4 = x + 6
✅ x/2 = 8
NOT Linear Equations:
❌ x² + 3 = 12 (has x²)
❌ x³ = 27 (has x³)
Linear vs Non-Linear Graphs
Interactive visualization — available in the full lesson
Linear equations always graph as straight lines!
⚖️ 2. The Main Principle: Balance!
🔑 Golden Rule:
Whatever you do to one side of the equation, you MUST do to the other side!
Our Goal:
Get the variable alone on one side of the equation. We call this isolating the variable.
How We Do It:
- Use inverse operations to undo what's done to the variable
- Keep the equation balanced
- Work step by step until x is alone
Think of an equation as a balanced scale — both sides must stay equal!