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].
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].
