To solve the equation \( \frac{3}{2}(4-8x) + 5x = 1 - 7x \), we first simplify the left-hand side:
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Distribute \( \frac{3}{2} \): \[ \frac{3}{2} \cdot 4 - \frac{3}{2} \cdot 8x = 6 - 12x \] So, the left side becomes: \[ 6 - 12x + 5x = 6 - 7x \]
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Now we can rewrite the equation: \[ 6 - 7x = 1 - 7x \]
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To isolate terms, add \( 7x \) to both sides: \[ 6 = 1 \]
This is a contradiction because \( 6 \) does not equal \( 1 \).
Since we ended up with a false statement, it means there are no solutions to the equation.
Thus, the answer is:
No solution.