To solve the equation \( \frac{3}{2} (4 - 8x) + 5x = 1 - 7x \), we can follow these steps:
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Distribute \( \frac{3}{2} \) in the expression \( \frac{3}{2} (4 - 8x) \): \[ \frac{3}{2} \cdot 4 - \frac{3}{2} \cdot 8x = 6 - 12x \] Therefore, 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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Add \( 7x \) to both sides: \[ 6 = 1 \]
Since we end up with a false statement (6 does not equal 1), this means that there are no values of \( x \) that satisfy the original equation. Thus, the equation has no solution.