Question

How many solutions does this equation have? Solve on paper and enter your answer on Zearn.
9x =
5
1
​
(45x+5)

Infinitely many solutions

One solution

No solutions

Answer 1

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:

1. Distribute the 5:

\[
5 \cdot (45x + 5) = 225x + 25
\]

So the equation becomes:

\[
9x = 225x + 25
\]

2. 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:

\[
-216x = 25
\]

3. 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**