To solve the equation \( \frac{3}{7} + \frac{1}{5}x - \frac{1}{4} = \frac{4}{5}x \), we will follow these steps:
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Rearranging the equation: First, we will isolate the terms involving \( x \) on one side of the equation.
\[ \frac{3}{7} - \frac{1}{4} = \frac{4}{5}x - \frac{1}{5}x \]
This simplifies to:
\[ \frac{3}{7} - \frac{1}{4} = \left( \frac{4}{5} - \frac{1}{5} \right)x \]
\[ \frac{3}{7} - \frac{1}{4} = \frac{3}{5}x \]
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Finding a common denominator for the left-hand side: The common denominator for 7 and 4 is 28. We will convert both fractions:
\[ \frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28} \] \[ \frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28} \]
Now, substituting back into the equation:
\[ \frac{12}{28} - \frac{7}{28} = \frac{3}{5}x \]
\[ \frac{12 - 7}{28} = \frac{3}{5}x \]
\[ \frac{5}{28} = \frac{3}{5}x \]
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Solving for \( x \): To isolate \( x \), multiply both sides by \( \frac{5}{3} \):
\[ x = \frac{5}{28} \cdot \frac{5}{3} = \frac{25}{84} \]
Thus, the solution is:
\[ \boxed{\frac{25}{84}} \]