The golden rule of equations is: Whatever you do to one side of the equation, you must do to the other side to maintain balance. This ensures the equality remains true throughout the solving process.
Understanding the Analogy
Think of an equation as a balanced scale. If you add weight to one side, you must add the same weight to the other side to keep it balanced. Similarly, if you remove weight from one side, you must remove the same weight from the other. This principle applies to all mathematical operations performed on an equation.
Applying the Golden Rule
The golden rule guides every step in solving an equation. This includes:
- Addition: Add the same number to both sides.
- Subtraction: Subtract the same number from both sides.
- Multiplication: Multiply both sides by the same number (excluding zero).
- Division: Divide both sides by the same number (excluding zero).
Example:
Let's solve the equation x + 5 = 10.
- To isolate
x, we need to subtract 5 from both sides:
x + 5 - 5 = 10 - 5 - This simplifies to:
x = 5
Importance of Maintaining Balance
Failing to apply the golden rule will result in an incorrect solution. The equation will become unbalanced, and the value of the unknown variable will be wrong.
Note: While the term "golden rule" is commonly used in elementary algebra, more advanced mathematical fields may use more formal terminology. The principle, however, remains the same. The linked Wikipedia article on the golden ratio discusses a mathematical concept unrelated to this algebraic principle.
