\( 1 \leftarrow \) Solve and check the equation. \[ \frac{x}{9}=\frac{5 x}{6}-13 \] What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \). B. The solution set is \( \{x \mid x \) is a real number \( \} \). C. The solution set is \( \varnothing \).

To solve the equation \( \frac{x}{9} = \frac{5x}{6} - 13 \), we first eliminate the fractions. Multiply both sides by 18 (the least common multiple of 9 and 6): \[ 18 \cdot \frac{x}{9} = 18 \cdot \left( \frac{5x}{6} - 13 \right) \] This simplifies to: \[ 2x = 15x - 234 \] Next, we move \( 15x \) to the left side: \[ 2x - 15x = -234 \] Which results in: \[ -13x = -234 \] Dividing both sides by -13 gives: \[ x = \frac{-234}{-13} = 18 \] Now let's check our solution by substituting \( x = 18 \) back into the original equation: Left side: \[ \frac{18}{9} = 2 \] Right side: \[ \frac{5 \cdot 18}{6} - 13 = 15 - 13 = 2 \] Since both sides are equal, the solution is verified. The solution set is \( \{ 18 \} \), so the correct choice is: A. The solution set is \( \{ 18 \} \).