To solve the equation \( \frac{3}{2} (4 - 8x) + 5x = 1 - 7x \), we can follow these steps:
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Distribute \( \frac{3}{2} \) to the terms inside the parentheses: \[ \frac{3}{2} \cdot 4 - \frac{3}{2} \cdot 8x = 6 - 12x \] So, the equation becomes: \[ 6 - 12x + 5x = 1 - 7x \]
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Combine like terms on the left side: \[ 6 - 7x = 1 - 7x \]
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Since both sides have \(-7x\), we can add \(7x\) to both sides to eliminate \(-7x\): \[ 6 = 1 \]
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This is a contradiction (since \(6\) does not equal \(1\)), which indicates that there is no solution to the equation.
Therefore, the conclusion is that the equation has no solution.