The principle that permits the removal of the same quantity from both sides of an equation without disrupting the equation’s balance is a foundational concept in mathematics. Formally stated, if a = b, then a – c = b – c. This implies that a numerical value can be subtracted from each side of a mathematical statement of equality, preserving the truth of that statement. For example, given the equation x + 5 = 10, subtracting 5 from both sides yields x + 5 – 5 = 10 – 5, which simplifies to x = 5. This demonstrates how the value of x can be isolated and determined through the application of this principle.
This principle offers several benefits in mathematical problem-solving. It enables the simplification of equations, making them easier to manipulate and solve. It is crucial for isolating variables and determining their values. The application of this rule is pervasive across various branches of mathematics, including algebra, calculus, and geometry. Its roots can be traced back to early algebraic manipulations, providing a bedrock upon which more complex mathematical concepts are built. Understanding this concept is fundamental for mastering algebraic techniques and furthering mathematical proficiency.
