Solve the following inequality and represent it on a number line: $\frac{x}{3} + 5 \geq \frac{x}{2} + 7$

(N/A) Given inequality: $\frac{x}{3} + 5 \geq \frac{x}{2} + 7$
Subtract $5$ from both sides:
$\frac{x}{3} \geq \frac{x}{2} + 2$
Subtract $\frac{x}{2}$ from both sides:
$\frac{x}{3} - \frac{x}{2} \geq 2$
Find a common denominator $(6)$:
$\frac{2x - 3x}{6} \geq 2$
$-\frac{x}{6} \geq 2$
Multiply both sides by $-6$ (remember to reverse the inequality sign when multiplying by a negative number):
$x \leq -12$
The solution set is $(-\infty, -12]$.
This is represented on the number line by a solid circle at $-12$ and a shaded line extending to the left.