The given expression represents a **union of two intervals** on the real number line:

- **(-∞, -2]**: This interval includes all real numbers from negative infinity up to and including -2.
- **[1, ∞)**: This interval includes all real numbers from 1 to positive infinity.

The symbol "∪" means "union," indicating that the solution set includes all numbers that are in either of these intervals.

### Interpretation:
- Numbers less than or equal to -2 or greater than or equal to 1 are part of the solution.
- The numbers between -2 and 1 (i.e., (-2, 1)) are **not** part of this set.

### Graphical representation:
On a number line, the set looks like this:
- A closed circle at -2, extending leftwards to negative infinity.
- A closed circle at 1, extending rightwards to positive infinity.

### Example of values in the set:
- Values like -3, -2, 1, 5, and 10 are in the set.
- Values like 0, -1, and -1.5 are not in the set.

Would you like further details on set notation or any other clarifications?

### Related Questions:
1. How do you graph the union of intervals on a number line?
2. What is the difference between open and closed intervals?
3. How do you represent the union and intersection of intervals?
4. Can we express this set in terms of inequalities?
5. How do interval notations apply in solving inequalities?

### Tip:
When working with intervals, remember that square brackets **[ ]** mean the endpoint is included (closed interval), while parentheses **( )** mean the endpoint is excluded (open interval).

The query submitted by the user: (−∞,−2]∪[1,∞)

Understand how to interpret and graph the union of intervals (-∞, -2] ∪ [1, ∞) on a number line. This topic covers set theory, interval notation, and the union of sets, with examples and a graphical representation. Ideal for students in Grades 9-12.

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