1. **State the problem:** Solve the equation $3x + 8y = 34$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving other terms to the opposite side and then dividing by the coefficient of $y$. 3. **Isolate $y$:** $$3x + 8y = 34$$ Subtract $3x$ from both sides: $$3x + 8y - 3x = 34 - 3x$$ $$8y = 34 - 3x$$ 4. **Divide both sides by 8:** $$y = \frac{34 - 3x}{8}$$ Show cancellation explicitly: $$y = \frac{\cancel{8} \cdot \frac{34 - 3x}{\cancel{8}}}{1} = \frac{34 - 3x}{8}$$ 5. **Final answer:** $$y = \frac{34 - 3x}{8}$$ This expresses $y$ in terms of $x$ clearly and completely.