The inequality is $\frac{x}{2}$ ≥ $\frac{5x-2}{3} - \frac{7x-3}{5}$ Multiply each term by L.C.M. of 2, 3, 5, i.e., by 30 $\frac{x}{2}$ × 30 ≥ $\frac{5x-2}{3} \times 30 - \frac{7x-3}{5}$ × 30 or, 15x ≥ 10(5x – 2) – 6(7x – 3) or, 15x ≥ 50x – 20 – 42x + 18 or, 15x – 8x ≥ –2 or, 7x ≥ –2 Dividing both sides by 7, x ≥ − $\frac{2}{7}$ ∴ The solution is $[-\frac{2}{7},\infty)$