Question
b) The interval notation of the inequality, \( -6
Ask by Ward Luna. in the United States
Feb 04,2025
Ask by Ward Luna. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The interval notation for \( -6 < x \leq -1 \) is \( (-6,\, -1] \).
Solution
The interval notation for the inequality \( -6 < x \leq -1 \) is:
\[
(-6,\, -1]
\]
**Explanation:**
- The parenthesis **(** indicates that \(-6\) is **not** included in the interval (since the inequality is strict \( x > -6 \)).
- The bracket **]** indicates that \(-1\) **is** included in the interval (since the inequality allows \( x \leq -1 \)).
So, the interval notation correctly represents all real numbers \( x \) that are greater than \(-6\) and up to (and including) \(-1\).
**Final Answer:**
\[
(-6,\, -1]
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
The interval notation for the inequality \( -6 < x \leq -1 \) can be written as \( (-6, -1] \). This notation indicates that \( x \) can take any value greater than \(-6\) but less than or equal to \(-1\), capturing the bounds perfectly while showing that \(-1\) is included in the interval. To visualize this interval, imagine a straight line representing the number line. You would place an open dot over \(-6\) (indicating that it is not included) and a closed dot over \(-1\) (indicating that it is part of the solution). This shows exactly where values are acceptable, making it super clear where \( x \) can play!
