1. **State the problem:** The sum of 9 and a certain number is one and a half times the original number. We need to find the number. 2. **Define the variable:** Let the certain number be $x$. 3. **Write the equation:** The sum of 9 and $x$ is equal to one and a half times $x$, so: $$9 + x = \frac{3}{2} x$$ 4. **Solve the equation:** Subtract $x$ from both sides: $$9 + \cancel{x} = \frac{3}{2} x - \cancel{x}$$ $$9 = \frac{3}{2} x - 1 x$$ Rewrite $1 x$ as $\frac{2}{2} x$ to subtract: $$9 = \frac{3}{2} x - \frac{2}{2} x = \frac{1}{2} x$$ 5. **Isolate $x$:** Multiply both sides by 2: $$2 \times 9 = 2 \times \frac{1}{2} x$$ $$18 = x$$ 6. **Answer:** The number is $18$. **Check:** Sum of 9 and 18 is 27. One and a half times 18 is $\frac{3}{2} \times 18 = 27$. The equation holds true. **Final answer:** $18$