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Answer :
To solve the inequality [tex]\(\frac{1}{3}n + 4.6 \leq 39.1\)[/tex], we need to determine the possible values for the variable [tex]\(n\)[/tex].
Here’s a step-by-step solution:
1. Start with the given 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 of the inequality:
[tex]\[
39.1 - 4.6 = 34.5
\][/tex]
So now the inequality is:
[tex]\[
\frac{1}{3}n \leq 34.5
\][/tex]
4. Multiply both sides by 3 to solve for [tex]\(n\)[/tex]:
[tex]\[
n \leq 34.5 \times 3
\][/tex]
5. Calculate the result:
[tex]\[
n \leq 103.5
\][/tex]
So, the possible values for the number [tex]\(n\)[/tex] are all the numbers that are less than or equal to 103.5. Therefore, the correct answer is [tex]\(n \leq 103.5\)[/tex].
Here’s a step-by-step solution:
1. Start with the given 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 of the inequality:
[tex]\[
39.1 - 4.6 = 34.5
\][/tex]
So now the inequality is:
[tex]\[
\frac{1}{3}n \leq 34.5
\][/tex]
4. Multiply both sides by 3 to solve for [tex]\(n\)[/tex]:
[tex]\[
n \leq 34.5 \times 3
\][/tex]
5. Calculate the result:
[tex]\[
n \leq 103.5
\][/tex]
So, the possible values for the number [tex]\(n\)[/tex] are all the numbers that are less than or equal to 103.5. Therefore, the correct answer is [tex]\(n \leq 103.5\)[/tex].
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