1. **Problem statement:** Solve the linear equation $$2X + 6 = 2(5X - 1)$$ for $X$. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$. Apply it to the right side: $$2(5X - 1) = 2 \times 5X - 2 \times 1 = 10X - 2$$ 3. **Rewrite the equation:** $$2X + 6 = 10X - 2$$ 4. **Bring all terms involving $X$ to one side and constants to the other:** $$2X - 10X = -2 - 6$$ 5. **Simplify both sides:** $$\cancel{2X} - 10X = -8$$ $$-8X = -8$$ 6. **Divide both sides by $-8$ to isolate $X$:** $$X = \frac{-8}{-8}$$ 7. **Simplify the fraction:** $$X = 1$$ **Final answer:** $$X = 1$$