Use complete sentences to describe why it is necessary to do the same thing to both sides of an equation to perf valid operations.

When solving equations, it is essential to perform the same operations on both sides to maintain the equality's validity. This principle ensures that the balance of the equation remains unchanged, much like a balanced scale where adding or removing weight from one side requires the same action on the other side to keep it level. If different operations were applied to each side, it would disrupt the equality, leading to incorrect solutions. By consistently applying the same mathematical operations to both sides, we preserve the original relationship between the variables, allowing us to isolate and solve for the desired unknown accurately. This approach guarantees that each step in the solution process is logically sound and that the final answer truly satisfies the initial equation.