Answer :
To solve the inequality [tex]\( \frac{1}{3}n + 4.6 \leq 39.1 \)[/tex], we need to find the possible values of [tex]\( n \)[/tex]. Here is a step-by-step solution:
1. Isolate the term with [tex]\( n \)[/tex]:
Start by subtracting 4.6 from both sides of the inequality to get rid of the constant term on the left side:
[tex]\[
\frac{1}{3}n \leq 39.1 - 4.6
\][/tex]
2. Perform the subtraction:
Calculate [tex]\( 39.1 - 4.6 \)[/tex]:
[tex]\[
39.1 - 4.6 = 34.5
\][/tex]
Now, the inequality looks like this:
[tex]\[
\frac{1}{3}n \leq 34.5
\][/tex]
3. Solve for [tex]\( n \)[/tex]:
To clear the fraction, multiply both sides of the inequality by 3:
[tex]\[
n \leq 3 \times 34.5
\][/tex]
4. Calculate the multiplication:
Perform the multiplication:
[tex]\[
3 \times 34.5 = 103.5
\][/tex]
This gives us the inequality:
[tex]\[
n \leq 103.5
\][/tex]
Therefore, the possible values for the number [tex]\( n \)[/tex] are those that are less than or equal to 103.5. Thus, the correct option is [tex]\( n \leq 103.5 \)[/tex].
1. Isolate the term with [tex]\( n \)[/tex]:
Start by subtracting 4.6 from both sides of the inequality to get rid of the constant term on the left side:
[tex]\[
\frac{1}{3}n \leq 39.1 - 4.6
\][/tex]
2. Perform the subtraction:
Calculate [tex]\( 39.1 - 4.6 \)[/tex]:
[tex]\[
39.1 - 4.6 = 34.5
\][/tex]
Now, the inequality looks like this:
[tex]\[
\frac{1}{3}n \leq 34.5
\][/tex]
3. Solve for [tex]\( n \)[/tex]:
To clear the fraction, multiply both sides of the inequality by 3:
[tex]\[
n \leq 3 \times 34.5
\][/tex]
4. Calculate the multiplication:
Perform the multiplication:
[tex]\[
3 \times 34.5 = 103.5
\][/tex]
This gives us the inequality:
[tex]\[
n \leq 103.5
\][/tex]
Therefore, the possible values for the number [tex]\( n \)[/tex] are those that are less than or equal to 103.5. Thus, the correct option is [tex]\( n \leq 103.5 \)[/tex].
