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

Responses

n≤112.7
n less than or equal to 112.7

n≤131.1
n less than or equal to 131.1

n≤103.5
n less than or equal to 103.5

n≤11.5
n less than or equal to 11.5

3 answers

To solve the inequality that Artem wrote, \( 13n + 4.6 \leq 39.1 \), we will isolate \( n \).

  1. First, we subtract 4.6 from both sides:

    \[ 13n \leq 39.1 - 4.6 \]

    Simplifying the right side:

    \[ 39.1 - 4.6 = 34.5 \]

    So we have:

    \[ 13n \leq 34.5 \]

  2. Next, we divide both sides by 13:

    \[ n \leq \frac{34.5}{13} \]

    Calculating the division:

    \[ n \leq 2.6538461538461537 \approx 2.65 \]

Thus, in decimal or fractional form, we can say \( n \leq 2.65 \).

Since none of the options provided explicitly include this solution, we should check if any of the response options approximate or make sense in the context of the problem. However, based on the steps above, the calculation of the inequality should lead to the conclusion that the number \( n \) must be less than or equal to \( 2.65 \). If your selection is considering rounded numbers, ensure to reevaluate the options directly against this value.

Please make sure you check back on the setup or assumptions involved with the 39.1 condition or refer back to how \( n \) was defined. The equation \( 13n + 4.6\) does not seem correctly derived from the initial problem statement concerning \(4.6 + \frac{1}{3}n \leq 39.1\). Keep in mind that \(n\) typically could represent values dictated by context.

If you need any further assistance, feel free to ask!

can you choose one of the respnses

I apologize for the confusion earlier. Let's clarify the setup based on Artem's inequality solution.

If we correctly derive the inequality from the problem statement:

\[ 4.6 + \frac{1}{3} n \leq 39.1 \]

We can isolate \( n \):

  1. Subtract \( 4.6 \) from both sides: \[ \frac{1}{3} n \leq 39.1 - 4.6 \] \[ \frac{1}{3} n \leq 34.5 \]

  2. Multiply both sides by \( 3 \) to solve for \( n \): \[ n \leq 34.5 \times 3 \] \[ n \leq 103.5 \]

From this correction, the appropriate response is:

n ≤ 103.5 n less than or equal to 103.5

This matches one of the given response options. Thank you for your patience!