College

The sum of 4.6 and one-third of a number is 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] represents the number, to help solve this problem. Solve his inequality.

A. [tex]n \leq 11.5[/tex]
B. [tex]n \leq 103.5[/tex]
C. [tex]n \leq 112.7[/tex]
D. [tex]n \leq 131.1[/tex]

Answer :

To solve the inequality [tex]\(\frac{1}{3}n + 4.6 \leq 39.1\)[/tex], we need to find the possible values for [tex]\(n\)[/tex]. Let's break down the steps:

1. Remove the constant term on the left side.
Start by subtracting 4.6 from both sides of the inequality to isolate the term with [tex]\(n\)[/tex]:
[tex]\[
\frac{1}{3}n \leq 39.1 - 4.6
\][/tex]

2. Calculate the right side.
Subtract 4.6 from 39.1:
[tex]\[
39.1 - 4.6 = 34.5
\][/tex]
So, the inequality becomes:
[tex]\[
\frac{1}{3}n \leq 34.5
\][/tex]

3. Eliminate the fraction.
To get rid of the fraction, multiply both sides of the inequality by 3:
[tex]\[
n \leq 3 \times 34.5
\][/tex]

4. Calculate the product.
Multiply 34.5 by 3:
[tex]\[
3 \times 34.5 = 103.5
\][/tex]

5. State the final inequality.
Therefore, the inequality is:
[tex]\[
n \leq 103.5
\][/tex]

This tells us that the value of the number [tex]\(n\)[/tex] must be at most 103.5. So the correct answer is [tex]\(n \leq 103.5\)[/tex].