Question

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.

Answer 1

To solve the inequality that Artem wrote, we'll start with the following equation:

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

First, we'll isolate the term with \( n \) by subtracting 4.6 from both sides:

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

Calculating the right-hand side:

\[
39.1 - 4.6 = 34.5
\]

So the inequality becomes:

\[
\frac{1}{3}n \leq 34.5
\]

Next, we eliminate the fraction by multiplying both sides by 3:

\[
n \leq 34.5 \times 3
\]

Calculating \( 34.5 \times 3 \):

\[
34.5 \times 3 = 103.5
\]

Thus, we have:

\[
n \leq 103.5
\]

The solution to the inequality is that the number \( n \) can take any value that is less than or equal to 103.5. Therefore, the possible values of the number are:

\[
n \in (-\infty, 103.5]
\]

This means the number \( n \) can be any value up to and including 103.5.