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 1/3n+4.6≤39.1

Question

, 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

Answer 1

To solve the inequality \( \frac{1}{3}n + 4.6 \leq 39.1 \), we can follow these steps:

1. Isolate the term involving \( n \): \[ \frac{1}{3}n + 4.6 \leq 39.1 \]

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

2. Eliminate the fraction by multiplying both sides by 3 (note that this does not change the direction of the inequality because we are multiplying by a positive number): \[ n \leq 34.5 \times 3 \] \[ n \leq 103.5 \]

The solution to the inequality is: \[ n \leq 103.5 \]

Therefore, the correct response is:

• n ≤ 103.5
• n less than or equal to 103.5