Questions: Solve the following rational equation. If there is no solution, state this as your answer. 1/5 n - 11/6 = 2/3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The solution set is x x ≠ (Simplify your answer. Use a comma to separate answers as needed.) B. The solution set is (Simplify your answer. Use a comma to separate answers as needed.) C. There is no solution.

Solution Steps

To solve the given rational equation, we need to isolate the variable \( n \). Start by eliminating the fractions by finding a common denominator, which in this case is 30. Multiply every term by 30 to clear the fractions. Then, solve the resulting linear equation for \( n \).

We start with the equation:

\[ \frac{1}{5} n - \frac{11}{6} = \frac{2}{3} \]

To eliminate the fractions, we multiply every term by the least common multiple of the denominators, which is 30:

\[ 30 \left( \frac{1}{5} n \right) - 30 \left( \frac{11}{6} \right) = 30 \left( \frac{2}{3} \right) \]

This simplifies to:

\[ 6n - 55 = 20 \]

Next, we isolate \( n \) by adding 55 to both sides:

\[ 6n = 20 + 55 \]

This simplifies to:

\[ 6n = 75 \]

Now, divide both sides by 6:

\[ n = \frac{75}{6} = 12.5 \]

Final Answer