What does the Subtraction Property of Equality state?

The Subtraction Property of Equality is a fundamental principle in algebra, indicating that if two quantities are equal, you can subtract the same value from both sides of the equation without changing the equality. This means that if one number equals another, subtracting a third number from both sides will still maintain the equality.

In this context, when it states "If a = b, then a - c = b - c," it illustrates that starting from two equal values (a and b), if you take some value (c) away from both a and b, their equality remains intact. This property is crucial for solving equations and allows for manipulation while preserving the balance of the equation.

Understanding this principle helps in solving more complex algebraic equations, as it reassures you that operations performed on both sides of an equation do not alter the underlying equality.