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 1/3 n + 4.6 ≤ 39.1, where n equals the number, to help solve this problem. Solve his inequality.(1 point)
A: n≤11.5
B: n≤112.7
C: n≤103.5
D: n≤131.1
C: n≤103.5
To solve the inequality, we will isolate the variable 'n' step by step.
The inequality is given as 1/3n + 4.6 ≤ 39.1.
1. Subtract 4.6 from both sides of the equation:
(1/3)n ≤ 39.1 - 4.6
This simplifies to:
(1/3)n ≤ 34.5
2. Multiply both sides of the inequality by 3 to eliminate the fraction:
3 * (1/3)n ≤ 3 * 34.5
This simplifies to:
n ≤ 103.5
Therefore, the solution to the inequality is n ≤ 103.5.
So, the answer is option C: n ≤ 103.5.
To solve the inequality 1/3n + 4.6 ≤ 39.1, we need to isolate n on one side of the inequality.
First, subtract 4.6 from both sides of the inequality:
1/3n ≤ 39.1 - 4.6
1/3n ≤ 34.5
Next, multiply both sides of the inequality by 3 to eliminate the fraction:
3 * (1/3n) ≤ 3 * 34.5
n ≤ 103.5
Therefore, the solution to the inequality is n ≤ 103.5.
So, the possible values of the number are all values less than or equal to 103.5.
The correct answer is C: n ≤ 103.5.