Problem 82 - Introductory Algebra for College Students

Question

What are additive inverses?

Step-by-Step Solution

Answer

The additive inverse of a number is the number that, when added to the original number, results in zero. For any number \(a\), its additive inverse is \(-a\).

Step 1: Understand the term 'inverse'

In mathematics, an 'inverse' of a number is something that, when combined with the original number using a specific operation, reverses the effect of that operation. In other words, if you apply an operation to a number and its inverse, you should get the identity element for that operation.

Step 2: Recognize the additive identity

For addition, the identity element is zero because adding zero to any number does not change the number. Symbolically, if \(a\) is any number, then \(a + 0 = a\).

Step 3: Define the additive inverse

Therefore, the additive inverse of a number is the number that, when added to the original number, results in zero. Symbolically, the additive inverse of a number \(a\) is often written as \(-a\) because \(a + (-a) = 0\).