Question

Solve the equation.
three sevenths plus one fifth x minus one fourth equals four fifths x
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Part 1
The solution is xequals
  
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Answer 1

To solve the equation \( \frac{3}{7} + \frac{1}{5}x - \frac{1}{4} = \frac{4}{5}x \), we will follow these steps:

1. **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:

\[
\frac{3}{7} - \frac{1}{4} = \left( \frac{4}{5} - \frac{1}{5} \right)x
\]

\[
\frac{3}{7} - \frac{1}{4} = \frac{3}{5}x
\]

2. **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:

\[
\frac{12}{28} - \frac{7}{28} = \frac{3}{5}x
\]

\[
\frac{12 - 7}{28} = \frac{3}{5}x
\]

\[
\frac{5}{28} = \frac{3}{5}x
\]

3. **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:

\[
\boxed{\frac{25}{84}}
\]