To solve the equation:
\[ \frac{2}{7} + \frac{1}{5}x - \frac{1}{4} = \frac{4}{5}x \]
First, let's isolate \(x\) on one side. Start by moving \(\frac{1}{5}x\) and \(\frac{1}{4}\) to the right side:
\[ \frac{2}{7} - \frac{1}{4} = \frac{4}{5}x - \frac{1}{5}x \]
Subtract the fractions on the left side and combine the \(x\) terms on the right side:
\[ \frac{2}{7} - \frac{1}{4} = \left(\frac{4}{5} - \frac{1}{5}\right)x \]
This simplifies to:
\[ \frac{2}{7} - \frac{1}{4} = \frac{3}{5}x \]
Next, we need to combine \(\frac{2}{7}\) and \(-\frac{1}{4}\). To do this, we need to find a common denominator. The least common multiple of 7 and 4 is 28.
Convert both fractions:
\[ \frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28} \] \[ -\frac{1}{4} = -\frac{1 \times 7}{4 \times 7} = -\frac{7}{28} \]
Now combine these:
\[ \frac{8}{28} - \frac{7}{28} = \frac{1}{28} \]
So now our equation is:
\[ \frac{1}{28} = \frac{3}{5}x \]
To isolate \(x\), multiply both sides by \(\frac{5}{3}\):
\[ x = \frac{1}{28} \times \frac{5}{3} = \frac{5}{84} \]
Thus, the solution is:
\[ x = \frac{5}{84} \]
Final answer:
x equals \(\frac{5}{84}\).