What does the subtraction axiom state?

The subtraction axiom states that if the same number is subtracted from both sides of an equation, the equality of the equation is maintained. This principle is foundational in algebra and helps ensure that equations remain balanced when performing operations. For instance, if you have an equation such as (x + 5 = 10), and you want to isolate (x), you can subtract 5 from both sides of the equation. This gives you (x + 5 - 5 = 10 - 5), simplifying to (x = 5). The integrity of the equation is preserved through this operation, which is the essence of the subtraction axiom.

The other choices involve different operations that maintain equality, such as addition, multiplication, and division, but do not specifically pertain to the act of subtraction, making them unrelated to the concept of the subtraction axiom.