The problem asks you to use the additive inverse property to fill in the blank. The additive inverse of a number is the number that, when added to the original number, gives a sum of zero.

In this case, the equation is: $\_\_ + (-7) = 0$

To solve this, we need to find the additive inverse of $-7$. The additive inverse of $-7$ is $+7$, because: $7 + (-7) = 0$

Thus, the blank should be filled with 7.

Let me know if you want more details or have any questions! Here are five related questions to expand your understanding:

1. What is the additive inverse of 5?
2. How would you solve $\_\_ + (-10) = 0$ using the additive inverse property?
3. What is the additive inverse of a positive number?
4. How can you verify if your solution is correct using addition?
5. What role does the zero play in the additive inverse property?

Tip: The additive inverse of any number $x$ is simply $-x$, and vice versa!