What principle describes the need for equal weights on both sides of an equation?

The principle that describes the necessity for equal weights on both sides of an equation is the Balance Principle. This principle underlines the fundamental concept that if one side of an equation is altered, the other side must be changed in a corresponding manner to maintain equality.

In mathematical terms, an equation represents a balance between two expressions. When you think of an equation as a scale, if you add or subtract a value from one side, you must do the same to the opposite side to keep the scale balanced. This is crucial for solving equations correctly, as any change to one side must be mirrored on the other side to preserve the equation's integrity.

The Balance Principle emphasizes that maintaining equilibrium is essential in equations, allowing for accurate solutions and reliable mathematical reasoning.