Question

Write the given statement in interval notation: (-5 < x < 2 or x ≥ 6) and (x ≤ -1 or x > 3).

A) (-5 < x < 2) or (x ≥ 6) or (x ≤ -1) or (x > 3)
B) (-5 ≤ x < 2) or (x ≥ 6) or (x ≤ -1) or (x > 3)
C) (-5 < x ≤ 2) or (x > 6) or (x ≤ -1) or (x > 3)
D) (-5 ≤ x ≤ 2) or (x > 6) or (x ≤ -1) or (x ≥ 3)

Answer 1

To write the given statement in interval notation, we have to break it down into separate intervals and combine them using the 'or' notation. The correct interval notation is (-5 ≤ x < 2) or (x ≥ 6) or (x ≤ -1) or (x > 3).

Step-by-step explanation:

To write the given statement in interval notation, we need to break it down into separate intervals and combine them using the notation 'or'.

The first part of the statement (-5 < x < 2 or x ≥ 6) can be written as (-5, 2) ∪ [6, ∞).

The second part of the statement (x ≤ -1 or x > 3) can be written as (-∞, -1] ∪ (3, ∞).

Combining both parts, we get (-5, 2) ∪ [6, ∞) ∪ (-∞, -1] ∪ (3, ∞), which matches option B.