Final answer:
Adding or subtracting equally from both sides of an equation keeps it true. The universality of math rules ensures the same result in any situation when these operations are applied correctly.
Step-by-step explanation:
Adding or subtracting numbers results in a true equation when the operations are applied equally to both sides of an equation, maintaining the balance. Just like a perfectly balanced see-saw, the equation remains valid if the same operation is conducted on both sides. This concept also applies when using numbers in any setting or context - the rules of mathematics are universally valid.
For fractions, vectors, and even simple whole numbers, the same principles apply. When you add or subtract the same number or quantity on both sides of an equation, it does not change the equality. This is why you can perform operations like simplification or solving variables, and reliably obtain true and accurate results as long as the operations are balanced on both sides.