When solving equations, what does the addition axiom allow you to do?

The addition axiom, also known as the property of equality for addition, states that if you have an equation, you can add the same number to both sides of the equation without changing the equality. This is fundamental in algebra as it allows you to manipulate equations to isolate variables and solve for them.

For example, if you start with the equation x = 5 and you add 3 to both sides, you arrive at x + 3 = 8, which is still a true statement. This property ensures that the relationship between the values on both sides remains consistent, thus making it easier to work through equations as you seek a solution.

This principle is integral for maintaining balance in equations, making it a key concept in the process of solving them. Understanding this axiom is essential for anyone working with algebraic expressions and equations.