## Elementary Algebra

As long as the same operation is performed on both sides of the equation, we can do anything to an equation to create an equivalent equation. This includes subtraction. For example, if we start with the equation $5+x=2$, which has the solution $-3$, and then subtract $10$ from both sides of the equation, we end up with a new equation: $x-5=-8$, which still has a solution of $-3$, making it an equivalent equation.