Question
\( x \leq \) Exactly right. High fivel 2. Show the full solution Express the answer to Question 1 in set notation, by choosing from the options and filling in the value of \( a \) Answer: \( x \in[a ; \infty) \) \( x \in(-\infty ; a) \) \( x \in(-\infty ; a] \) \( x \in[-\infty ; a] \)
Ask by Potter Vargas. in South Africa
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x \in (-\infty; a] \)
Solution
To solve the inequality \( x \leq a \), we need to express the solution in set notation.
1. **Understanding the inequality**: The inequality \( x \leq a \) means that \( x \) can take any value that is less than or equal to \( a \).
2. **Set notation**: In set notation, we express the solution as a set of all possible values of \( x \) that satisfy the inequality.
- The values of \( x \) that satisfy \( x \leq a \) include all numbers from negative infinity up to and including \( a \).
3. **Choosing the correct option**: The correct set notation for the solution \( x \leq a \) is:
\[
x \in (-\infty; a]
\]
Thus, the answer is:
\[
x \in (-\infty; a]
\]
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Simplify this solution Bonus Knowledge
To express \( x \leq a \) in set notation, we need to identify the correct interval. The solution indicates that \( x \) can take on any value less than or equal to \( a \). Therefore, the interval would include \( a \) and stretch to negative infinity, which is expressed as \( x \in (-\infty ; a] \). Now, let's give a high five for logic! When you see this kind of inequality, remember that it covers all values from negative infinity up to and including \( a \). It’s like having an all-you-can-eat buffet where everyone is welcome up to the limit, including the limit itself—yummy!
