Final answer:
The correct set in interval notation for x is (-∞, -3) ∪ [0, ∞), which is expressed as separated intervals demonstrating that all numbers less than -3 as well as all numbers greater than or equal to 0 are included.
Step-by-step explanation:
The set x in interval notation represents the set of all real numbers that are either less than -3 or greater than or equal to 0. This can be expressed in interval notation as two separate intervals. The first interval, (-∞, -3), represents all numbers less than -3, and these are not included in the set, which is why parentheses are used instead of brackets. The second interval, [0, ∞), represents all numbers greater than or equal to 0 and is shown with a bracket at 0 to indicate that 0 is included in the set.
Therefore, the correct answer is the one combining these two intervals with the union symbol, which is option b: (-∞, -3) ∪ [0, ∞).