To solve the equation \(-7(k + 5) = 3k - (8k - 1)\), let's start by simplifying both sides.
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Distribute on the left side: \[ -7(k + 5) = -7k - 35 \]
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Simplify the right side: \[ 3k - (8k - 1) = 3k - 8k + 1 = -5k + 1 \]
Now, we can rewrite the equation: \[ -7k - 35 = -5k + 1 \]
Next, let's isolate \(k\). Add \(7k\) to both sides: \[ -35 = 2k + 1 \]
Now, subtract \(1\) from both sides: \[ -35 - 1 = 2k \] \[ -36 = 2k \]
Now, divide by \(2\): \[ k = -18 \]
Thus, the solution is: \[ \boxed{-18} \]