Given that n satisfy the inequality 1/5 (n + 4) + 1 <_ 2/6 (n + 1) select the smallest possible value of n if n is a perfect square​



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.

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