Additive inverse
The additive inverse of a number is a number that is the same distance from 0 on the number line, but in the opposite direction. It can also be thought of as the number that you need to add to a number in order for the result to be 0.
Examples
In the number line below, -3 and 3 are additive inverses. If we add the other value to either of the two values, the result will be 0.
-3 + 3 = 0
3 - 3 = 0
The same is true of the other corresponding values on the number line; 5 and -5, 4 and -4, 2 and -2, 1 and -1, and even 0 and 0, are all also additive inverses.
Additive inverses in algebra
When trying to determine the additive inverse of an expression, rather than just an integer, multiply the entire expression by -1. This changes the sign of all the terms in the expression, and will sum to 0 when added to the original expression.
Examples
1. Find the additive inverse of x + 1:
-1 × (x + 1) = -x - 1
We can confirm that -x - 1 is the additive inverse by adding it to x + 1:
x + 1 + (-x - 1) = x - x + 1 - 1 = 0
2. Find the additive inverse of x2 + 3x - 4:
-1 × (x2 + 3x - 4) = -x2 - 3x + 4
Confirm the additive inverse:
x2 + 3x - 4 - x2 - 3x + 4 = 0