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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:

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

Answer :

To solve the inequality [tex]\(\frac{1}{3}n + 4.6 \leq 39.1\)[/tex], you can follow these steps:

1. Subtract 4.6 from both sides:
[tex]\[
\frac{1}{3}n + 4.6 - 4.6 \leq 39.1 - 4.6
\][/tex]
Simplifying the left side, this becomes:
[tex]\[
\frac{1}{3}n \leq 34.5
\][/tex]

2. Multiply both sides by 3 to isolate [tex]\(n\)[/tex]:
[tex]\[
3 \times \frac{1}{3}n \leq 3 \times 34.5
\][/tex]
This simplifies to:
[tex]\[
n \leq 103.5
\][/tex]

Therefore, the possible values of the number [tex]\(n\)[/tex] are all numbers less than or equal to 103.5. The correct answer is [tex]\(n \leq 103.5\)[/tex].

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Rewritten by : Jeany

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