The Balance Principle

An equation is a scale in balance. Whatever you do to one side, you must do to the other — add, subtract, multiply, or divide. This balance principle is the single rule behind every equation-solving method. Master it, and you can solve any linear equation.

For 4(x - 3) = 20: first distribute — 4x - 12 = 20. Then add 12: 4x = 32. Then divide by 4: x = 8. Each step is justified by doing the same thing to both sides. No step changes what x equals; it only reveals the answer more clearly.