Subtracting Negative Numbers

You also need to be able to subtract negative numbers comfortably. If you consider negative numbers as "debts", then you remove a debt when you subtract a negative number. Removing a debt of 4 dollars is like being given 4 dollars. This explains why the equation $5-(-4)=5+4$ holds: subtracting negative four is the same as adding positive four.

The symbols $-(-4)$ also represent "the additive inverse OF (the additive inverse of $4$)". Our work with additive inverses can help you write this expression in a different and simpler way. After all, the additive inverse of $4$ is $-4$, and now the additive inverse of $-4$ is, by definition, a number that results in zero when added to $-4$. Of course, the additive inverse of $-4$ is $4$ itself. All of this tells us that $-(-4)=4$. In the next section, we will discuss multiplying and dividing negative numbers.

Source: Algebra2Go, https://www.youtube.com/watch?v=mA6CCfaXTDc
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