Question: (6y + \frac{3}{2} x = 15
1. **Stating the problem:** Solve the equation $$6y + \frac{3}{2} x = 15$$ for $y$ in terms of $x$.
2. **Formula and rules:** To isolate $y$, we need to move the term involving $x$ to the other side and then divide by the coefficient of $y$.
3. **Isolate $y$:**
$$6y = 15 - \frac{3}{2} x$$
4. **Divide both sides by 6:**
$$y = \frac{15 - \frac{3}{2} x}{6}$$
5. **Simplify the fraction:**
$$y = \frac{15}{6} - \frac{\frac{3}{2} x}{6}$$
6. **Simplify each term:**
$$y = \frac{15}{6} - \frac{3}{2} \times \frac{x}{6}$$
7. **Simplify fractions:**
$$y = \frac{15}{6} - \frac{3}{12} x$$
8. **Reduce fractions:**
$$y = \frac{5}{2} - \frac{1}{4} x$$
**Final answer:**
$$y = \frac{5}{2} - \frac{1}{4} x$$