1. **State the problem:** Solve the linear equation $2y - x = 4$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by performing algebraic operations such as addition, subtraction, multiplication, or division. 3. **Isolate $y$:** Starting with the equation: $$2y - x = 4$$ Add $x$ to both sides: $$2y - x + x = 4 + x$$ which simplifies to: $$2y = 4 + x$$ 4. **Divide both sides by 2 to solve for $y$:** $$y = \frac{4 + x}{2}$$ Show the cancellation step: $$y = \frac{\cancel{2}(2) + x}{\cancel{2} \times 1}$$ This simplifies to: $$y = 2 + \frac{x}{2}$$ 5. **Final answer:** $$y = 2 + \frac{x}{2}$$ This expresses $y$ in terms of $x$ clearly and simply.