The principle stating that if both sides of an equation are multiplied by the same non-zero number, the equality remains valid. Formally, for any real numbers a, b, and c, if a = b, then ac = bc. For instance, given the equation x/2 = 5, multiplying both sides by 2 maintains the balance, resulting in x = 10.
This fundamental concept is crucial in algebraic manipulation, enabling the isolation of variables and the simplification of equations. Its application ensures that the solution set of an equation remains unchanged during the solving process. The principle is a cornerstone of equation solving strategies and has been utilized since the development of algebraic notation, forming a basis for advanced mathematical operations.
