Pregunta
Express the set in interval notation. \[ \{x \mid x<5 \text { or } x \geq 15\} \]
Ask by Christensen Li. in the United States
Feb 02,2025
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The set in interval notation is \((-\infty, 5) \cup [15, \infty)\).
Solución
The set \(\{x \mid x < 5 \text{ or } x \geq 15\}\) can be expressed in interval notation by considering each condition separately:
1. \(x < 5\) corresponds to the interval \((-\infty, 5)\).
2. \(x \geq 15\) corresponds to the interval \([15, \infty)\).
Since the condition uses "or," we take the union of these two intervals. Therefore, the set in interval notation is:
\[
(-\infty, 5) \cup [15, \infty)
\]
**Answer:**
\[
(-\infty,\ 5) \cup [\,15,\ \infty\,)
\]
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Simplifique esta solución The Deep Dive
The set can be expressed in interval notation as \((- \infty, 5) \cup [15, \infty)\). This means that all real numbers less than 5 are included in the first interval, while the numbers from 15 onwards, including 15 itself, are included in the second interval. To visualize it, imagine a number line: everything to the left of 5 is covered in the first segment, and starting at 15 and continuing to the right, all those numbers are included in the second. It's a nice way to represent parts of the number line efficiently!
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