1. \textbf{Problem statement:} We add 9 yellow balls. We have drawn at least one more yellow ball than the total of blue and red balls combined.\n\n2. \textbf{Understanding the problem:} Let $y$ be the number of yellow balls drawn, $b$ the number of blue balls, and $r$ the number of red balls. The problem states: $$y \geq b + r + 1$$\n\n3. \textbf{Adding 9 yellow balls:} If initially there were $y_0$ yellow balls, after adding 9, the new number of yellow balls is $$y = y_0 + 9$$\n\n4. \textbf{Inequality after adding:} The condition becomes $$y_0 + 9 \geq b + r + 1$$\n\n5. \textbf{Rearranging:} $$y_0 \geq b + r + 1 - 9$$\n$$y_0 \geq b + r - 8$$\n\n6. \textbf{Interpretation:} Initially, the number of yellow balls drawn must be at least $b + r - 8$ to satisfy the condition after adding 9 yellow balls.\n\n\textbf{Final answer:} The inequality $$y \geq b + r + 1$$ holds after adding 9 yellow balls if initially $$y_0 \geq b + r - 8$$.