# 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 x^{2} + 3x - 4:

-1 × (x^{2} + 3x - 4) = -x^{2} - 3x + 4

Confirm the additive inverse:

x^{2} + 3x - 4 - x^{2} - 3x + 4 = 0