To analyze the work done by the student, let's first review the steps accurately and identify where potential mistakes may have occurred.
The original equation is: \[ 4(2 - 3x) = x - 2(2x + 1) \]
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Distributing on both sides:
- Left side: \( 4(2) - 4(3x) = 8 - 12x \)
- Right side: \( x - 2(2x + 1) = x - 4x - 2 = -3x - 2 \)
So the equation simplifies to: \[ 8 - 12x = -3x - 2 \]
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Rearranging the equation: The student rewrote it as: \[ 8 - 12x = -3x - 2 \] (This step appears correctly done.)
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Combining like terms: The next step would be to move all terms involving \(x\) to one side and the constant terms to the other side. We can add \(12x\) and \(2\) to both sides to get: \[ 8 + 2 = 12x - 3x \] This gives: \[ 10 = 9x \] Now divide by \(9\): \[ x = \frac{10}{9} \]
The student concluded that the equation had "No Solution". However, the correct solution is \(x = \frac{10}{9}\). Thus, it appears there was a mistake in understanding or interpreting the equation at some point.
Conclusion: The correct equation solved should show that it has one unique solution \(x = \frac{10}{9}\). Therefore, the student's final answer is incorrect based on their solution process, and the equation does indeed have a solution.