To solve the equation \( x - 13 = -13 \), we need to isolate \( x \).
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Start with the equation: \[ x - 13 = -13 \]
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Add 13 to both sides: \[ x - 13 + 13 = -13 + 13 \]
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Simplifying both sides gives: \[ x = 0 \]
Therefore, the integer that makes the addition sentence true is \( \boxed{0} \).