To subtract the expression \((-9q - 5) - (-3q + 1)\), follow these steps:
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Distribute the negative sign across the second expression: \[ -9q - 5 + 3q - 1 \]
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Combine like terms:
- Combine the \(q\) terms: \(-9q + 3q = -6q\)
- Combine the constant terms: \(-5 - 1 = -6\)
So, the result is: \[ -6q - 6 \]
Thus, \((-9q - 5) - (-3q + 1) = -6q - 6\).