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15) \( x \leq 2 \)

Ask by French Bolton. in the United States
Feb 26,2025

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The solution to \( x \leq 2 \) is all real numbers less than or equal to 2, which can be written as \( (-\infty, 2] \).

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The inequality given is \( x \leq 2 \). This means that the variable \( x \) can take any value that is less than or equal to 2. ### Solution Steps: 1. **Understanding the Inequality**: - The symbol \( \leq \) indicates that \( x \) can be equal to 2 or any number less than 2. 2. **Set Representation**: - In set notation, this can be represented as \( x \in (-\infty, 2] \). 3. **Graphical Representation**: - On a number line, you would draw a solid dot at 2 (indicating that 2 is included) and shade everything to the left of 2. ### Conclusion: The solution to the inequality \( x \leq 2 \) is all real numbers less than or equal to 2, which can be expressed as \( (-\infty, 2] \).

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Beyond the Answer

The inequality \( x \leq 2 \) means that \( x \) can take any value that is less than or equal to 2. Picture a number line: all the points to the left of 2, including 2 itself, are part of the solution. This type of inequality often shows up in various math problems, especially in linear programming and optimization scenarios! In real-life situations, inequalities like this can model constraints. For example, if you're planning an event and need the number of attendees to be 2 or fewer for a specific room capacity, this inequality clearly illustrates that limit. You can visualize holding a cozy gathering where intimate conversations are the norm rather than a large, boisterous party—just think of the possibilities!

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