Final answer:
To solve the inequality -3x - 8 > -26, we find that x must be less than 6. The largest integer that satisfies this condition is 5.
Step-by-step explanation:
The question asks us to find the largest integer that fits the inequality described by "eight less than the product of -3 and an integer is greater than -26". To solve this, let's represent the unknown integer with the variable x. The inequality can be expressed as -3x - 8 > -26. Now, we will solve for x:
- Add 8 to both sides of the inequality to isolate the term with x: -3x > -18.
- Divide both sides by -3, remembering to reverse the inequality sign since we're dividing by a negative number: x < 6.
Since x must be less than 6 and it should be an integer, the largest integer possible that satisfies this inequality is 5.