marcusking wrote: None are always true.

But the question doesn't ask 'which of the following is always true?' It asks 'which of the following must be true?' There's quite a difference, and this is the reason why you cannot simply plug in different values of x into each inequality. To illustrate, consider the following question:

If x = 1, what must be true?
A) x < 1
B) x < 0
C) x = 5
D) -1 < x < 1
E) x < 1000

That's a perfectly valid question, and the answer is E; if x is equal to 1, then it certainly must be true that x is less than 1000. It doesn't matter that there are numbers less than 1000 which cannot be equal to x.

So, in the question above, we aren't looking for an inequality that describes every possible solution for x; we're only looking for an inequality which contains every possible solution for x, perhaps along with some values that are not solutions for x.

To find the solutions to the inequality, I graphed y = |x-1| and y = (x-5)^2 to see that the only possible solutions for x are close to the value x=5. Since x is an integer, we can find all possible values: x = 4, 5, 6, 7. It's still a badly designed question, because the problem now is that there are then two correct answers - D) and E) - since if x is one of the values 4, 5, 6 or 7, it clearly must be true that x > 1, and also that x > 0.