1. **State the problem:** Solve the equation $X \times 39 + 6 = X \times 50 - 6$ for $X$. 2. **Write the equation:** $$39X + 6 = 50X - 6$$ 3. **Isolate terms with $X$ on one side and constants on the other:** Subtract $39X$ from both sides: $$\cancel{39X} + 6 = 50X - 6 - \cancel{39X}$$ which simplifies to $$6 = 11X - 6$$ 4. **Add 6 to both sides to isolate the term with $X$:** $$6 + 6 = 11X - 6 + 6$$ $$12 = 11X$$ 5. **Divide both sides by 11 to solve for $X$:** $$\frac{12}{\cancel{11}} = X \times \frac{\cancel{11}}{11}$$ which simplifies to $$X = \frac{12}{11}$$ **Final answer:** $$X = \frac{12}{11}$$