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≤103.5
n less than or equal to 103.5

n≤11.5
n less than or equal to 11.5

n≤131.1
n less than or equal to 131.1

n≤112.7
n less than or equal to 112.7
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Answer 1

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

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

   Calculating the right side: \[ 39.1 - 4.6 = 34.5 \] So the inequality becomes: \[ \frac{1}{3}n \leq 34.5 \]

2. Next, multiply both sides by 3 to solve for \( n \): \[ n \leq 34.5 \times 3 \]

   Calculate \( 34.5 \times 3 \): \[ 34.5 \times 3 = 103.5 \]

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

Thus, the correct response is: n ≤ 103.5

Answer 2

Twelve less than four-fifths of a number is more than 24. What are all the possible values of the number? Lucia wrote the inequality 4/5n−12>24
, where n equals the number, to help solve this problem. Solve her inequality.(1 point)
Responses

n>15
n greater than 15

n>45
n greater than 45

n>28.8
n greater than 28.8

n>9.6