What is the inverse of 5 under addition?

The inverse of a number under a given operation is a number that, when combined with the original number using that operation, results in the identity element for that operation. In the case of addition, the identity element is 0.

To find the inverse of 5 under addition, we need to identify a number that, when added to 5, yields 0. Mathematically, this means we need to solve the equation:

5 + x = 0.

To find the value of x, we can rearrange the equation:

x = -5.

Thus, -5 is the number that satisfies this equation, confirming that -5 is indeed the additive inverse of 5. When you add 5 and -5, the result is 0, which is the identity element for addition. This principle is fundamental in mathematics, illustrating how inverses work in relation to identity elements for different operations.