1. **State the problem:** Solve the linear equation $2y + x = 3$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we need to get $y$ alone on one side of the equation. This involves subtracting $x$ from both sides and then dividing both sides by 2. 3. **Isolate $y$:** $$2y + x = 3$$ Subtract $x$ from both sides: $$2y + x - x = 3 - x$$ $$2y = 3 - x$$ 4. **Divide both sides by 2:** $$y = \frac{3 - x}{2}$$ Show cancellation explicitly: $$y = \frac{\cancel{2} \cdot \frac{3 - x}{\cancel{2}}}{1} = \frac{3 - x}{2}$$ 5. **Final answer:** $$y = \frac{3 - x}{2}$$ This expresses $y$ in terms of $x$ for the given linear equation.