Solve the following inequality and represent it on a number line: $\frac{3x}{2} + 15 \leq \frac{2x}{3} + 6$

(N/A) Given inequality: $\frac{3x}{2} + 15 \leq \frac{2x}{3} + 6$
Subtract $15$ from both sides: $\frac{3x}{2} \leq \frac{2x}{3} - 9$
Subtract $\frac{2x}{3}$ from both sides: $\frac{3x}{2} - \frac{2x}{3} \leq -9$
Find a common denominator $(6)$: $\frac{9x - 4x}{6} \leq -9$
$\frac{5x}{6} \leq -9$
Multiply both sides by $6$: $5x \leq -54$
Divide by $5$: $x \leq -10.8$
The solution set is $(-\infty, -10.8]$.
On the number line,this is represented by a solid circle at $-10.8$ with a line extending to the left.