Write the interval of points that are less than -2 using interval notation
The correct answer and explanation is :
The interval notation for points that are less than -2 is:
[
(-\infty, -2)
]
Explanation:
- Understanding Interval Notation
Interval notation is a way to represent a set of numbers along a number line. It consists of:
- Parentheses (( )) or Brackets ([ ]) to indicate whether endpoints are included or not.
- Infinity symbols ((\infty) or (-\infty)) to represent unbounded intervals.
- Identifying the Given Condition
The problem asks for numbers that are less than -2, meaning we are looking for all numbers that are strictly smaller than -2. - Choosing the Correct Interval
- The left boundary: Since we are dealing with numbers that extend indefinitely in the negative direction, we use (-\infty) as the lower bound.
- The right boundary: Since we are not including -2 (just numbers less than -2), we use a parenthesis (() instead of a bracket ([)], meaning -2 itself is not included.
- Why Not Include -2?
- If the problem said “less than or equal to -2,” we would include -2 and use ([-2]).
- However, because it only says “less than -2,” -2 is excluded.
- Final Answer
Thus, the correct answer is:
[
(-\infty, -2)
]
This notation captures all real numbers that are strictly less than -2.