To solve the inequality given by Artem, we start with:
\[ 13n + 4.6 \leq 39.1 \]
First, we isolate \(n\) by subtracting 4.6 from both sides:
\[ 13n \leq 39.1 - 4.6 \]
Calculating the right side:
\[ 39.1 - 4.6 = 34.5 \]
So we have:
\[ 13n \leq 34.5 \]
Next, we divide both sides by 13:
\[ n \leq \frac{34.5}{13} \]
Calculating the division:
\[ n \leq 2.6538461538461537 \]
Rounding this gives:
\[ n \leq 2.65 \]
Therefore, the inequality shows that the possible values for the number \(n\) must be less than or equal to approximately 2.65.
However, checking the responses provided and based on the arithmetic, it seems there might be a typo in Artem's original setup regarding the factor of \(n\). If we instead wrote the original problem correctly using one-third of a number, it would actually lead to a different equation. The original equation derived from "the sum of 4.6 and one-third a number is equal to at most 39.1" would mean we should rewrite it using \( \frac{1}{3}n \):
\[ 4.6 + \frac{1}{3}n \leq 39.1 \]
Now subtract 4.6:
\[ \frac{1}{3}n \leq 39.1 - 4.6 \]
Calculating the right side again:
\[ 39.1 - 4.6 = 34.5 \]
Thus, we get:
\[ \frac{1}{3}n \leq 34.5 \]
Multiplying both sides by 3:
\[ n \leq 34.5 \times 3 = 103.5 \]
So, the solution shows that \(n\) must be less than or equal to 103.5, so:
\[ n \leq 103.5 \]
The correct inference from the given responses would therefore be:
n ≤ 103.5.