Final answer:
The transitive property of equality allows for the same operation to be performed on both sides of an equation while maintaining equality, a fundamental concept in algebra used in solving equations.
Step-by-step explanation:
The properties that allow you to perform the same operation to both sides of an equation while maintaining equality is known as the transitive property of equality. This principle is part of basic algebraic rules that state if two values are equal, operations done to one side must also be done to the other to maintain balance. For example, multiplication or division by the same number on both sides of an equation does not change the equality. If an equation starts as 'A = B', and you multiply both sides by 'C', resulting in 'AC = BC', the equality holds true.
Using this principle allows us to solve equations by strategically performing operations to isolate a variable on one side of an equation. These operations may include addition, subtraction, multiplication, or division. It is important, however, to ensure that every term on either side of the equation is subject to the same operation.