Step 1 :

The given inequality is : $ \large\frac{x}{2} \geq \frac{(5x-2)}{3} - \frac{(7x-3)}{5}$

$=> \large\frac{x}{2} \geq \frac{5(5x-2)-3(7x-3)}{15}$

$=> \large\frac{x}{2} \geq \large\frac{25 x -10 -21 x +9}{15}$

$=> \large\frac{x}{2} \geq \large\frac{4x-5}{15}$

Multiplying both sides of the inequality by positive number 30.

$=> 15 x \geq 2(4x-1)$

$15 x \geq 8x-2$

Adding $-8x$ on both sides of the inequality

$=> 15 x - 8x \geq 8x -2 -8x$

=> $ 7x \geq -2$

Dividing both sides of the inequality by positive number 7.

$=> x \geq \large\frac{-2}{7}$

Step 2:

All number greater than or equal to $\large\frac{-2}{7}$from the solution for the given inequality .

The solution set is $[-2/7, \infty)$

The graphical representation is