If [x] denotes the least integer greater than or equal to x and [x/2] = 0, which of the following could be the value of x? A. - 2B. - 3/2C. 1/2D. 1E. 2

B) - 3/2

Step-by-step explanation:

If [x/2]=0 then x/2 is a number such that the least integer greater than or equal to x/2 is 0. We can rewrite this as the inequality x/2≤0. Then, the value of x in C, D and E is wrong because they are positive numbers, then x/2 would be a positive number which contradicts this inequality.

Now, 0 is the least integer that satisfies this inequality, therefore we cannot have that x/2≤-1 since - 1 is an integer and - 1-1. This discards A as wrong, because for x=-2, x/2=-1, contrary to x/2>-1.

Thus B is the right answer. To verify, if x=-3/2, then x/2=-3/4 and we have that - 1<-3/4≤0 as required.