1. **State the problem:** Solve the equation $2 - X = 10 + X$ for $X$. 2. **Write down the equation:** $$2 - X = 10 + X$$ 3. **Goal:** Isolate $X$ on one side of the equation. 4. **Add $X$ to both sides to eliminate $-X$ on the left:** $$2 - \cancel{X} + X = 10 + X + X$$ $$2 = 10 + 2X$$ 5. **Subtract 10 from both sides to isolate terms with $X$ on the right:** $$2 - 10 = 10 - 10 + 2X$$ $$-8 = 2X$$ 6. **Divide both sides by 2 to solve for $X$:** $$\frac{-8}{\cancel{2}} = \frac{2X}{\cancel{2}}$$ $$-4 = X$$ 7. **Final answer:** $$X = -4$$