1. **State the problem:** Solve the equation $$\frac{5x}{2} = 11 + \frac{2x}{3}$$ for $x$. 2. **Identify the goal:** We want to isolate $x$ on one side of the equation. 3. **Eliminate fractions:** Multiply both sides by the least common denominator (LCD) of 2 and 3, which is 6, to clear the denominators. $$6 \times \frac{5x}{2} = 6 \times \left(11 + \frac{2x}{3}\right)$$ 4. **Simplify each term:** $$6 \times \frac{5x}{2} = \cancel{6} \times \frac{5x}{\cancel{2}} \times 3 = 15x$$ $$6 \times 11 = 66$$ $$6 \times \frac{2x}{3} = \cancel{6} \times \frac{2x}{\cancel{3}} \times 2 = 4x$$ So the equation becomes: $$15x = 66 + 4x$$ 5. **Isolate $x$ terms:** Subtract $4x$ from both sides: $$15x - 4x = 66 + 4x - 4x$$ $$\cancel{15x} - \cancel{4x} = 66 + \cancel{4x} - \cancel{4x}$$ $$11x = 66$$ 6. **Solve for $x$:** Divide both sides by 11: $$\frac{11x}{11} = \frac{66}{11}$$ $$\cancel{11}x = 6$$ $$x = 6$$ **Final answer:** $x = 6$