1. **State the problem:** Solve the equation $13 - 9(x+1) = 2x - 9$ for $x$. 2. **Apply the distributive property:** Expand $-9(x+1)$ to get $-9x - 9$. 3. **Rewrite the equation:** $13 - 9x - 9 = 2x - 9$ 4. **Simplify the left side:** $13 - 9 = 4$, so the equation becomes $4 - 9x = 2x - 9$ 5. **Collect like terms:** Add $9x$ to both sides: $4 = 2x + 9x - 9$ which simplifies to $4 = 11x - 9$ 6. **Isolate the variable term:** Add $9$ to both sides: $4 + 9 = 11x$ which is $13 = 11x$ 7. **Solve for $x$:** Divide both sides by $11$: $$x = \frac{13}{11}$$ **Final answer:** $x = \frac{13}{11}$