What example illustrates the addition axiom?

The addition axiom, also known as the property of equality for addition, states that if two expressions are equal, you can add the same value to both sides of the equation without changing the equality.

In the correct example, which illustrates this axiom, the equation X - 15 + 15 = 30 + 15 demonstrates how the same value (in this case, 15) is added to both sides of the equation. This maintains the equality, which is the fundamental idea behind the addition axiom.

On the left side, the -15 and +15 cancel each other out, simplifying to X on the left, while on the right side, 30 + 15 equals 45. This leads to the conclusion that X equals 45, showing the process of applying the addition axiom effectively and correctly. This illustrates the principle that manipulating both sides of an equation equivalently keeps it balanced, a critical concept in algebra and arithmetic.