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 an equation, performing the same operation on both sides is essential because it preserves the equality of the equation. For example, if you have an equation like 2x + 3 = 7 and you subtract 3 from both sides, you maintain the balance, making it 2x = 4. This allows you to isolate the variable without altering the relationship between the two sides. By ensuring that both sides are treated equally, you avoid introducing errors that could lead to incorrect solutions. Think of it like a seesaw: if you add a weight to one side, you must also add an equivalent weight to the other to keep it balanced. This fundamental principle allows you to confidently solve equations systematically.