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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 1/3n+4.6≤39.1 , 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≤11.5 n less than or equal to 11.5 n≤112.7 n less than or equal to 112.7 n≤131.1

1 answer

To solve the inequality \( \frac{1}{3}n + 4.6 \leq 39.1 \), we will first isolate the term involving \( n \).

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

  2. Next, to isolate \( n \), multiply both sides by \( 3 \) (note that since \( 3 \) is positive, the direction of the inequality does not change): \[ n \leq 3 \times 34.5 \] \[ n \leq 103.5 \]

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

From the options provided, the correct response is:

  • \( n \leq 103.5 \)