Solve the given inequality and show the graph of the solution on a number line:
$\frac{x}{2} \geq \frac{5x-2}{3} - \frac{7x-3}{5}$

(N/A) Given inequality: $\frac{x}{2} \geq \frac{5x-2}{3} - \frac{7x-3}{5}$
$\Rightarrow \frac{x}{2} \geq \frac{5(5x-2) - 3(7x-3)}{15}$
$\Rightarrow \frac{x}{2} \geq \frac{25x - 10 - 21x + 9}{15}$
$\Rightarrow \frac{x}{2} \geq \frac{4x - 1}{15}$
Multiplying both sides by $30$:
$\Rightarrow 15x \geq 2(4x - 1)$
$\Rightarrow 15x \geq 8x - 2$
$\Rightarrow 15x - 8x \geq -2$
$\Rightarrow 7x \geq -2$
$\Rightarrow x \geq -\frac{2}{7}$
The solution set is $[-\frac{2}{7}, \infty)$. The graphical representation is a solid circle at $-\frac{2}{7}$ with a line extending to the right.