Final answer:
The greatest possible integer that satisfies the inequality 3.8x < 24.1 is 6. After dividing 24.1 by 3.8, we find that x must be less than 6.34210526, making 6 the largest integer that meets the criteria.
Step-by-step explanation:
The student asks for the greatest possible integer solution of the inequality 3.8x < 24.1. To find this, we first solve for x by dividing both sides of the inequality by 3.8, which gives us x < 24.1 / 3.8. Performing the division we get x < 6.34210526, which means x can take any lesser value but not reach or exceed 6.34210526.
Since we are looking for the greatest integer solution, we look for the whole number just below our result. That number is 6 because it's the highest integer less than 6.34210526, and satisfying the given inequality.
Therefore, the greatest possible integer solution to the inequality 3.8x < 24.1 is 6.