To solve the inequality \( \frac{x}{13} < \frac{4}{5} \), we need to isolate \( x \).
- Start by multiplying both sides of the inequality by 13 (since 13 is positive, the direction of the inequality does not change):
\[ x < 13 \cdot \frac{4}{5} \]
- Calculate the right side:
\[ 13 \cdot \frac{4}{5} = \frac{52}{5} \]
- To convert \( \frac{52}{5} \) to a decimal, divide 52 by 5:
\[ \frac{52}{5} = 10.4 \]
Therefore, the solution to the inequality is:
\[ x < \frac{52}{5} \quad \text{or} \quad x < 10.4 \]
Now, let's convert \( \frac{52}{5} \) into a more suitable form if necessary. The numerical value is equivalent to:
\[ x < 10\frac{2}{5} \]
The answer options given do not match directly with our result. Thus, there seems to be a focus on interpreting \( \frac{52}{5} \) correctly in the response options.
From the response options provided, none are exact. However, the closest correct interpretation is:
x < 13 \( \frac{4}{5} \) (since \( 13 \times \frac{4}{5} = \frac{52}{5} = 10.4 \))
So, the most suitable response from the options listed would be:
x < 13 \( \frac{4}{5} \).
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