Solve the Fraction Equation: Finding X in 1/3x = 1/9

To solve this problem, we'll follow these steps:

• Identify the given fraction equation.
• Multiply both sides of the equation by the reciprocal of the coefficient of $x$.
• Simplify to isolate $x$.

Now, let's work through these steps:
Step 1: The problem gives us the equation $\frac{1}{3} x = \frac{1}{9}$.
Step 2: We multiply both sides by 3 to eliminate the fraction on the left side:

$3 \times \frac{1}{3} x = 3 \times \frac{1}{9}$

Step 3: Simplifying both sides results in:

$x = \frac{3}{9}$

Further simplification of $\frac{3}{9}$ yields:

$x = \frac{1}{3}$

Therefore, the solution to the problem is $\frac{1}{3}$.