1. **State the problem:** Solve the equation $3x = 2y + 3$ for $x$ in terms of $y$. 2. **Formula and rules:** To isolate $x$, we need to divide both sides of the equation by 3. Remember, when dividing both sides of an equation by the same nonzero number, the equality remains true. 3. **Isolate $x$:** $$3x = 2y + 3$$ Divide both sides by 3: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{2y + 3}{3}$$ 4. **Simplify:** $$x = \frac{2y + 3}{3}$$ 5. **Final answer:** $$x = \frac{2y + 3}{3}$$ This expresses $x$ in terms of $y$ clearly and simply.