The expression \( (-\infty, 0) \cup [-6, 2) \) represents a union of two intervals on the number line. Let's break it down:

1. **First Interval**: \( (-\infty, 0) \) includes all numbers less than 0, but not 0 itself. This interval goes from negative infinity to 0, and since it uses parentheses, 0 is excluded.
  
2. **Second Interval**: \( [-6, 2) \) includes all numbers between -6 and 2. It includes -6 (because of the square bracket), but it does not include 2 (because of the parentheses).

3. **Union ( ∪ )**: The union of these two intervals means that any number that belongs to either interval is included. So, the complete set of numbers in this union is:

   \[
   (-\infty, 0) \cup [-6, 2) = (-\infty, 0) 
   \]

   This is because \( [-6, 2) \) is a subset of \( (-\infty, 0) \), and we don't need to include 0 or any number greater than 0.

Thus, the final answer is:

\[
(-\infty, 2)
\]

Would you like further clarification?

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Here are 5 questions to expand your understanding:

1. What is the difference between open and closed intervals?
2. How would the union change if the intervals were \( [0, 2] \cup [-6, 0] \)?
3. How do you find the intersection of two intervals?
4. How would you represent the set \( [1, 3] \cup (4, 5] \)?
5. Can a union of two intervals be disjoint?

**Tip**: A square bracket \( [ \) or \( ] \) means the number is included, while a parenthesis \( ( \) or \( ) \) means it is excluded.

The query submitted by the user: (-∞,0) ∪ [-6,2)

Learn how to solve the union of intervals (-∞, 0) ∪ [-6, 2) with a clear step-by-step breakdown. This problem covers key mathematical concepts, including set theory and interval notation. Suitable for students in Grades 9-11.

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