To simplify the expression \((-13x - 15) - (-9x + 16)\), we start by distributing the negative sign:
\[ (-13x - 15) - (-9x + 16) = -13x - 15 + 9x - 16 \]
Now, combine the like terms:
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Combine the \(x\) terms: \[ -13x + 9x = -4x \]
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Combine the constant terms: \[ -15 - 16 = -31 \]
Putting it all together, we have:
\[ -4x - 31 \]
Thus, the expression simplifies to \(-4x - 31\).
Now, comparing this with the provided options, we see that it matches option C. \(-4x - 31\).
Therefore, the answer is C.
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