How many integers satisfy the condition |x|≤−5
The question asks how many integers have |x| less than -5. |x| is the distance from origin. So it can't be negative.
⇒ There are no integers which satisfy this relation.
How many integers satisfy the condition |x| ≥ 2 and |x|≤ 6
How many integers satisfy the condition 0≤23[x]≤1