Final answer:
To achieve the greatest value for x, you should use the largest digit, 9, as the minuend and the smallest digit, 1, as the subtrahend, resulting in 9 - 1 = 8.
Step-by-step explanation:
To find the greatest value for x using the digits 1 to 9 without repeating any digit, we want the largest digit in the place of x and the smallest possible digit subtracted from it. Therefore, the answer is 9 - 1 = 8. Using the largest possible value for x and the smallest digit ensures that the subtraction yields the highest result.
From the given options, 9 - 8 = 1 does not give us the highest value of x. Instead, 9 - 1 = 8 provides the largest result and therefore is the correct answer. The reasoning behind this solution also implies a deeper understanding of mathematical operations, specifically subtraction, where a larger minuend and a smaller subtrahend maximize the difference.