The inequality \(\displaystyle\frac{5x - 2}{3} - \frac{7x - 3}{5} \gt \frac{x}{4}\) holds when
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(x \in (4, \infty)\)
Multiplying both sides by the LCM 60, a positive number, keeps the sign of the inequality:
\(20(5x - 2) - 12(7x - 3) \gt 15x\)
\(100x - 40 - 84x + 36 \gt 15x\)
\(16x - 4 \gt 15x\)
\(x \gt 4\)
So \(x \in (4, \infty)\). The inequality is strict, so 4 itself is not included.