### Video Transcript

Find the additive inverse of a
half.

The additive inverse of a number 𝑎
is a number that when added to 𝑎 equals zero. For any real number, this just
reverses the sign. The additive inverse of 𝑎 is
negative 𝑎 as 𝑎 plus negative 𝑎 equals zero.

This is because the opposite to a
positive number is negative. And likewise, the opposite to a
negative number is positive. If we let the additive inverse of a
half equal 𝑥, we know that a half plus 𝑥 equals zero.

Subtracting a half from both sides
of the equation gives us 𝑥 equals negative a half. This means that a half plus
negative half equal zero.

Therefore, the additive inverse of
a half is negative half. This method can be used for any
real number.

For example, the additive inverse
of positive three is negative three. Likewise, the additive inverse of
negative five is positive five. These results give us the general
solution that the additive inverse of 𝑎 is negative 𝑎.