The inequality $\frac{5x - 2}{3} - \frac{7x - 3}{5} > \frac{x}{4}$ holds when

\( x \in (4, \infty) \)

The correct answer is Option (2) → \( x \in (4, \infty) \)

$\text{Given: }\frac{5x-2}{3}-\frac{7x-3}{5}>\frac{x}{4}.$

$\text{LCM of denominators: }60.$

$\Rightarrow 20(5x-2) - 12(7x-3) > 15x.$

$100x - 40 - 84x + 36 > 15x.$

$16x - 4 > 15x.$

$x - 4 > 0.$

$x > 4.$

$\text{Solution: }x>4.$