To determine how many solutions the equation \(-4(5 - 3x) = 12x + 20\) has, we will first simplify both sides of the equation.
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Distribute on the left side: \[ -4(5 - 3x) = -4 \cdot 5 + (-4) \cdot (-3x) = -20 + 12x \] So the left side becomes: \[ -20 + 12x \]
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Now, our equation looks like: \[ -20 + 12x = 12x + 20 \]
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Next, let's subtract \(12x\) from both sides: \[ -20 = 20 \]
This simplifies to a statement that is false (\(-20\) does not equal \(20\)).
Since we have arrived at a contradiction, it means that the original equation has no solutions.
The answer is: A) no solution.