1. **State the problem:** Solve the linear equation $X + 3y = 6$ for $X$ in terms of $y$. 2. **Formula and rules:** To isolate $X$, subtract $3y$ from both sides of the equation. 3. **Intermediate work:** $$X + 3y = 6$$ Subtract $3y$ from both sides: $$X + \cancel{3y} - \cancel{3y} = 6 - 3y$$ 4. **Simplify:** $$X = 6 - 3y$$ 5. **Explanation:** We moved the term $3y$ to the right side by subtracting it from both sides, isolating $X$. This gives the expression for $X$ in terms of $y$. **Final answer:** $$X = 6 - 3y$$