Write the following expression as a single interval.

Ask by Herrera Sanders. in the United States

Jan 23,2025

Question

Write the following expression as a single interval. $$ (-\infty, 1) \cap[-5,2] $$

UpStudy AI · Accepted Answer

To find the intersection of the intervals $$ (-\infty, 1) $$ and $$[-5, 2]$$, we need to determine the set of all real numbers that satisfy both conditions simultaneously.

1. **First Interval ($$-\infty, 1$$)**:
   - This represents all real numbers less than 1.

2. **Second Interval ($$[-5, 2]$$)**:
   - This represents all real numbers from -5 to 2, inclusive.

**Intersection**:
- We are looking for numbers that are both less than 1 and between -5 and 2.
- The overlap of these two conditions is the set of numbers that are greater than or equal to -5 and less than 1.

Therefore, the intersection $$ (-\infty, 1) \cap [-5, 2] $$ is the interval:

$$
[-5, 1)
$$

**Answer:** $$[-5,\,1)$$
The intersection of the intervals $$(-\infty, 1)$$ and $$[-5, 2]$$ is $$[-5, 1)$$.

Write the following expression as a single interval.

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