Answer :
Step-by-step explanation:
To find the smallest possible value of ( n ), we'll first simplify the given inequality:
[tex]\[
\frac{1}{5}(n + 4) + 1 \leq \frac{2}{6}(n + 1)
\]
[/tex]
Simplify each side:
[tex]\[
\frac{1}{5}(n + 4) + 1 \leq \frac{2}{6}(n + 1)
\]
[/tex]
Multiply each side by 15 to clear the denominators:
[tex]\[
3n + 12 + 15 \leq 5n + 5
\][/tex]
Simplify:
[tex]\[
3n + 27 \leq 5n + 5
\][/tex]
Subtract (3n) from both sides:
[tex]\[
27 \leq 2n + 5
\]
[/tex]
Subtract 5 from both sides:
[tex]\[
22 \leq 2n
\][/tex]
Divide both sides by 2:
[tex]\[
11 \leq n
\][/tex]
Since ( n ) has to be a perfect square, and the smallest perfect square greater than or equal to 11 is 16, the smallest possible value of ( n ) is 16.
