By definition, an additive inverse is the expression you add to another expression to get zero. In other words, the additive inverse is an expression's negated value.
The additive inverse can be used to turn a subtraction problem into an addition problem for convenience. For example let's have
[tex](5x+10)-(-5x-20)[/tex]
You can get the additive inverse of -5x-20 by distributing -1 to each term. It's additive inverse will be 5x+20.
Now that we have this inverse, we can easily turn the expression to an addition problem:
[tex](5x+10)+(5x+20)[/tex]
At this point we can just simply combine like terms and arrive at the answer (10x+30).
Additive inverses also play a role on systems of linear equations.
