Final answer:
To find the greatest integer that satisfies the inequality, 5x + 13 < 24, we solve for x to get x < 2.2, which means the greatest integer is 2.
Step-by-step explanation:
The question asks to find the greatest integer in the set of values that satisfies the inequality where the sum of five times a number and 13 is less than 24. First, let's express the inequality algebraically: 5x + 13 < 24. Next, we solve for x by subtracting 13 from both sides, giving us 5x < 11. Dividing both sides by 5 yields x < 2.2. However, since we are looking for the greatest integer that satisfies this inequality, we must choose the largest integer less than 2.2, which is 2.