1. **State the problem:** Solve the linear equation $2y + x = 6$ 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 $y$:** $$2y + x = 6$$ Subtract $x$ from both sides: $$2y + \cancel{x} - x = 6 - x$$ $$2y = 6 - x$$ 4. **Divide both sides by 2:** $$\frac{2y}{\cancel{2}} = \frac{6 - x}{2}$$ $$y = \frac{6 - x}{2}$$ 5. **Final answer:** $$y = \frac{6 - x}{2}$$ This expresses $y$ in terms of $x$ for the given linear equation.