College

The sum of 4.6 and one-third of a number is equal to at most 39.1. What are all the possible values of the number?

Artem wrote the inequality [tex]\frac{1}{3}n + 4.6 \leq 39.1[/tex], where [tex]n[/tex] equals the number, to help solve this problem.

Solve his inequality.

Answer :

To solve the inequality Artem wrote, follow these steps:

1. Start with the inequality:
[tex]\(\frac{1}{3} n + 4.6 \leq 39.1\)[/tex].

2. Subtract 4.6 from both sides to isolate the term with [tex]\(n\)[/tex]:
[tex]\(\frac{1}{3} n \leq 39.1 - 4.6\)[/tex].

3. Calculate the right side:
[tex]\(39.1 - 4.6 = 34.5\)[/tex].

4. Therefore, the inequality becomes:
[tex]\(\frac{1}{3} n \leq 34.5\)[/tex].

5. To solve for [tex]\(n\)[/tex], multiply both sides of the inequality by 3 to eliminate the fraction:
[tex]\(n \leq 3 \times 34.5\)[/tex].

6. Calculate the result:
[tex]\(3 \times 34.5 = 103.5\)[/tex].

So, the possible values for the number [tex]\(n\)[/tex] are:
[tex]\(n \leq 103.5\)[/tex].

This means the number can be any value less than or equal to 103.5.