For all z, [z] denotes the least integer greater than or equal to z.

"Least integer greater than or equal to z implies that [z] >= z but [z] takes the least value that it can.

So if z = 0.3, [z] = 1
If z = 1.98, [z] = 2

Ques: Is [x] = 0?
When will [x] be 0? When -1 < x <= 0
So we need to know whether -1 < x <= 0?

Stmnt 2: [x + 0.5] = 1

Say, x + 0.5 = z
Given: [z] = 1
If [z] = 1, then we know that 0 < z <= 1. Note that if z is 0, [z] = 0. If z > 1, then [z] > 1 too.

This implies that 0 < x + 0.5 <= 1
Subtracting 0.5 from the inequality, we get
-0.5 < x <= 0.5
We know that x lies between -0.5 and 0.5. Some of these values lie in the -1 to 0 range and some do not. Hence we can't say whether x will lie in the -1 to 0 range.
Not sufficient alone.