The inequality is

x

2

≥

(5x−2)

3

−

(7x−3)

5

Multiply each term by L.C.M. of 2, 3, 5, i.e., by 30

x

2

× 30 ≥

(5x−2)

3

×30−

(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 ≥ −

2

7

∴ The solution is [−

2

7

,∞)