To solve the equation \(-8(3x + 6) = 7(-4x + 1)\), let's first distribute on both sides of the equation.
Starting with the left side:
\[ -8(3x + 6) = -8 \cdot 3x - 8 \cdot 6 = -24x - 48 \]
Now, the right side:
\[ 7(-4x + 1) = 7 \cdot -4x + 7 \cdot 1 = -28x + 7 \]
Now we rewrite the equation with the distributed terms:
\[ -24x - 48 = -28x + 7 \]
Next, we will isolate \(x\). First, we can add \(28x\) to both sides:
\[ -24x + 28x - 48 = 7 \]
This simplifies to:
\[ 4x - 48 = 7 \]
Now we add \(48\) to both sides:
\[ 4x = 7 + 48 \]
Simplifying this gives:
\[ 4x = 55 \]
Now, we divide both sides by \(4\):
\[ x = \frac{55}{4} \]
Thus, the solution to the equation is:
\[ \boxed{\frac{55}{4}} \]
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