Let's solve the equation step by step. The equation given is:
\[ 9x = 5 \cdot (45x + 5) \]
First, we can simplify the right side of the equation:
- Distribute the 5:
\[ 5 \cdot (45x + 5) = 225x + 25 \]
So the equation becomes:
\[ 9x = 225x + 25 \]
- Next, we want to isolate \(x\) by moving all \(x\) terms to one side of the equation. Subtract \(225x\) from both sides:
\[ 9x - 225x = 25 \]
This simplifies to:
\[ -216x = 25 \]
- Now, divide both sides by -216 to solve for \(x\):
\[ x = \frac{25}{-216} \quad \text{or} \quad x = -\frac{25}{216} \]
Since we found a single value for \(x\), we conclude that there is exactly one solution.
Thus, the answer is:
One solution