What does the Division Property of Equality allow us to do?

The Division Property of Equality states that if you have an equation and you divide both sides by the same nonzero number, the two sides remain equal. This property is critical in solving equations because it allows the simplification of equations to isolate the variable. For example, if you have the equation 8x = 24, dividing both sides by 8 gives you x = 3, maintaining the equality of the original equation.

Using the Division Property correctly ensures that the solution set remains unchanged, allowing for accurate and consistent results in algebraic manipulations. It is essential to remember that the number you divide by must not be zero, as division by zero is undefined.