The sum of 4.6 and one-third a number is equal to at most 39.1. What are all the possible values of the number? Artem wrote the inequality 13n+4.6≤39.1

Question

, where n equals the number, to help solve this problem. Solve his inequality.(1 point)
Responses

n≤103.5
n less than or equal to 103.5

n≤112.7
n less than or equal to 112.7

n≤11.5
n less than or equal to 11.5

n≤131.1

Answer 1

To solve Artem's inequality \( 13n + 4.6 \leq 39.1 \), we will first isolate \( n \).

1. Start with the inequality: \[ 13n + 4.6 \leq 39.1 \]

2. Subtract \( 4.6 \) from both sides: \[ 13n \leq 39.1 - 4.6 \] \[ 13n \leq 34.5 \]

3. Now, divide both sides by \( 13 \): \[ n \leq \frac{34.5}{13} \]

4. Calculate \( \frac{34.5}{13} \): \[ \frac{34.5}{13} = 2.653846153846154 \approx 2.65 \]

Thus, \[ n \leq 2.65 \]

Now let's look for approximate values in your provided options since it seems there might have been a misunderstanding or error in their formation. Based on our calculations, among the provided responses, none accurately represent the outcome.

So ensuring clarity, we confirm the solution: The correct inequality solved is:

\[ n \leq 2.65 \]

The options provided are inconsistent with this result. However, the methodology is correctly illustrated for achieving the solution.