1. **State the problem:** Solve the equation $2x - 1 = 10 + 2x - 8$ for $x$. 2. **Write the equation clearly:** $$2x - 1 = 10 + 2x - 8$$ 3. **Simplify the right side:** $$10 - 8 = 2$$ So the equation becomes: $$2x - 1 = 2 + 2x$$ 4. **Subtract $2x$ from both sides to isolate constants:** $$2x - 1 - \cancel{2x} = 2 + 2x - \cancel{2x}$$ Which simplifies to: $$-1 = 2$$ 5. **Analyze the result:** The statement $-1 = 2$ is false, which means there is no value of $x$ that satisfies the equation. **Final answer:** The equation has **no solution** because it simplifies to a false statement.