Pregunta
Express the given interval as an inequality in terms of \( x \), and select the graph of the interval. \( (-3,9) \) The inequality is \( \square \).
Ask by Black Christensen. in the United States
Jan 29,2025
Solución de tutoría real
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The inequality is \( -3 < x < 9 \).
Solución
To express the interval \( (-3, 9) \) as an inequality in terms of \( x \), you'll consider all real numbers \( x \) that are greater than \(-3\) and less than \(9\).
**The inequality is:**
\[
-3 < x < 9
\]
**Graph Explanation:**
On a number line, this interval is represented by an open circle at \(-3\) and an open circle at \(9\), with a line connecting all the points between them. The open circles indicate that \(-3\) and \(9\) are **not** included in the interval.
```
<----|----|----|----|----|----|----|----|----|---->
-5 -4 -3 -2 -1 0 1 2 3 4 ... 9
(=======================)
```
- **( )** represents an open circle at both ends.
- The shaded region between \(-3\) and \(9\) indicates all values of \(x\) that satisfy the inequality \( -3 < x < 9 \).
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Extra Insights
The inequality represented by the interval \((-3, 9)\) is \(-3 < x < 9\). This notation indicates that \( x \) can take any value between \(-3\) and \(9\), but does not include the endpoints themselves (as indicated by the parentheses). To represent this graphically, you would typically draw a number line and shade the region between \(-3\) and \(9\), using open circles at \(-3\) and \(9\) to indicate that these values are not included in the interval.
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