We are given that $n$ is an integer. We need to find the greatest possible value of $n$ that satisfies the inequality $3n - 25 < 2$.

1. Problem Description

We are given that $n$ is an integer. We need to find the greatest possible value of $n$ that satisfies the inequality $3n - 25 < 2$.

2. Solution Steps

We need to solve the inequality for $n$:

$3n - 25 < 2$

Add 25 to both sides of the inequality:

$3n - 25 + 25 < 2 + 25$

$3n < 27$

Divide both sides of the inequality by 3:

$\frac{3n}{3} < \frac{27}{3}$

$n < 9$

Since $n$ is an integer, the greatest possible value of $n$ that is less than 9 is

8.

3. Final Answer

The greatest possible value of $n$ is 8.