The additive inverse of a number is it's opposite.
So if a number is positive, it's additive inverse is the negative of that number. If a number is negative, it's additive inverse would be the positive value.
Examples:
If the number is 5, the additive inverse is -5
If the number is -3, the additive inverse would be 3
When you add a negative and a positive number of the same value, the answer would be 0.