Question
The solution is: \( x<=-11 / 2 \) 2 Super work! Write the answer in interval notation. INSTRUCTION: You can write infinity, \( \infty \), as 'oo", two small solution letter o's.
Ask by Bernard Martin. in South Africa
Mar 08,2025
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Answer
The solution in interval notation is \( (-\infty, -\frac{11}{2}] \).
Solution
To express the solution \( x \leq -\frac{11}{2} \) in interval notation, we need to identify the range of values that \( x \) can take.
1. The inequality \( x \leq -\frac{11}{2} \) indicates that \( x \) can take any value less than or equal to \(-\frac{11}{2}\).
2. In interval notation, this is represented as:
- The left endpoint is \(-\infty\) (or "oo") since \( x \) can go down to negative infinity.
- The right endpoint is \(-\frac{11}{2}\), and since the inequality includes equality (the "less than or equal to" part), we use a square bracket to indicate that \(-\frac{11}{2}\) is included in the interval.
Thus, the interval notation for the solution is:
\[
(-oo, -\frac{11}{2}]
\]
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Simplify this solution Beyond the Answer
The interval notation for the solution \( x \leq -\frac{11}{2} \) is \( (-\infty, -\frac{11}{2}] \). This means all values of \( x \) from negative infinity up to and including \(-\frac{11}{2}\) are part of the solution set. Ensure to remember that interval notation uses parentheses and brackets to indicate whether endpoints are included. Round brackets \( ( ) \) mean that the endpoint is not included, while square brackets \( [ ] \) mean it is included. In this case, since we're including \(-\frac{11}{2}\), we use the square bracket!
