To solve the inequality \( \frac{x}{13} < \frac{4}{5} \), we can start by isolating \( x \).
- Multiply both sides of the inequality by 13 to eliminate the fraction:
\[ x < 13 \cdot \frac{4}{5} \]
- Calculate the right side:
\[ 13 \cdot \frac{4}{5} = \frac{13 \cdot 4}{5} = \frac{52}{5} \]
So now we have:
\[ x < \frac{52}{5} \]
Converting \( \frac{52}{5} \) to a mixed number:
\[ \frac{52}{5} = 10 \frac{2}{5} \]
Thus, the solution to the inequality is:
\[ x < \frac{52}{5} \quad \text{or} \quad x < 10 \frac{2}{5} \]
Now, let's look at the options you provided:
- \( x < 10 \frac{2}{5} \) ✅ (This is correct)
- \( x < \frac{4}{65} \) ❌
- \( x > \frac{52}{5} \) ❌
- \( x < 13 \frac{4}{5} \) ❌ (This is not relevant to the solution)
The correct answer is \( x < 10 \frac{2}{5} \).