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Find the additive inverse of a half.
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The additive inverse of a number 𝑎 is a number that when added to 𝑎 equals zero.
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For any real number, this just reverses the sign.
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The additive inverse of 𝑎 is negative 𝑎 as 𝑎 plus negative 𝑎 equals zero.
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This is because the opposite to a positive number is negative.
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And likewise, the opposite to a negative number is positive.
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If we let the additive inverse of a half equal 𝑥, we know that a half plus 𝑥 equals zero.
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Subtracting a half from both sides of the equation gives us 𝑥 equals negative a half.
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This means that a half plus negative half equal zero.
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Therefore, the additive inverse of a half is negative half.
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This method can be used for any real number.
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For example, the additive inverse of positive three is negative three.
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Likewise, the additive inverse of negative five is positive five.
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These results give us the general solution that the additive inverse of 𝑎 is negative 𝑎.