The Inequality X ≤ − 8 X \leq -8 X ≤ − 8 Would Represent Which Of The Following Values?A. { 8 , 5 , 0 } \{8, 5, 0\} { 8 , 5 , 0 } B. { − 6 , − 7 , − 8 } \{-6, -7, -8\} { − 6 , − 7 , − 8 } C. { − 10 , − 9 , − 8 } \{-10, -9, -8\} { − 10 , − 9 , − 8 } D. None Of These Choices Are Correct.

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Introduction

In mathematics, inequalities are used to represent relationships between variables. They are an essential part of mathematical expressions and are used to describe various conditions. In this article, we will focus on the inequality $x \leq -8$ and its representation. We will explore the values that this inequality represents and discuss the options provided.

Understanding the Inequality

The inequality $x \leq -8$ represents all values of $x$ that are less than or equal to $-8$. This means that any value of $x$ that is greater than $-8$ is not included in the solution set. To understand this better, let's consider some examples.

Example 1: Values Less Than -8

Let's consider the value $x = -10$. Since $-10$ is less than $-8$, it satisfies the inequality $x \leq -8$. Therefore, $x = -10$ is a valid solution.

Example 2: Values Greater Than -8

Now, let's consider the value $x = 5$. Since $5$ is greater than $-8$, it does not satisfy the inequality $x \leq -8$. Therefore, $x = 5$ is not a valid solution.

Analyzing the Options

Now that we have a better understanding of the inequality $x \leq -8$, let's analyze the options provided.

Option A: $\{8, 5, 0\}$

This option includes values that are greater than $-8$. As we discussed earlier, these values do not satisfy the inequality $x \leq -8$. Therefore, this option is incorrect.

Option B: $\{-6, -7, -8\}$

This option includes values that are less than or equal to $-8$. As we discussed earlier, these values satisfy the inequality $x \leq -8$. Therefore, this option is correct.

Option C: $\{-10, -9, -8\}$

This option includes values that are less than or equal to $-8$. As we discussed earlier, these values satisfy the inequality $x \leq -8$. Therefore, this option is correct.

Option D: None of these choices are correct.

Based on our analysis, we can see that options B and C are correct. Therefore, this option is incorrect.

Conclusion

In conclusion, the inequality $x \leq -8$ represents all values of $x$ that are less than or equal to $-8$. The correct options are B and C, which include values that satisfy the inequality. We hope this article has provided a clear understanding of the inequality $x \leq -8$ and its representation.

Key Takeaways

• The inequality $x \leq -8$ represents all values of $x$ that are less than or equal to $-8$.
• Values that are greater than $-8$ do not satisfy the inequality $x \leq -8$.
• Options B and C are correct, as they include values that satisfy the inequality $x \leq -8$.

Further Reading

If you are interested in learning more about inequalities and their representation, we recommend checking out the following resources:

• Khan Academy: Inequalities
• Mathway: Inequalities
• Wolfram MathWorld: Inequalities

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Introduction

In our previous article, we explored the inequality $x \leq -8$ and its representation. We discussed the values that this inequality represents and analyzed the options provided. In this article, we will provide a Q&A section to further clarify any doubts or questions you may have.

Q&A

Q: What is the meaning of the inequality $x \leq -8$?

A: The inequality $x \leq -8$ represents all values of $x$ that are less than or equal to $-8$. This means that any value of $x$ that is greater than $-8$ is not included in the solution set.

Q: What values satisfy the inequality $x \leq -8$?

A: Values that are less than or equal to $-8$ satisfy the inequality $x \leq -8$. Examples of such values include $-10$, $-9$, and $-8$.

Q: What values do not satisfy the inequality $x \leq -8$?

A: Values that are greater than $-8$ do not satisfy the inequality $x \leq -8$. Examples of such values include $5$, $8$, and $0$.

Q: How do I determine if a value satisfies the inequality $x \leq -8$?

A: To determine if a value satisfies the inequality $x \leq -8$, simply compare the value to $-8$. If the value is less than or equal to $-8$, it satisfies the inequality.

Q: What are some examples of values that satisfy the inequality $x \leq -8$?

A: Some examples of values that satisfy the inequality $x \leq -8$ include $-10$, $-9$, $-8$, $-7$, and $-6$.

Q: What are some examples of values that do not satisfy the inequality $x \leq -8$?

A: Some examples of values that do not satisfy the inequality $x \leq -8$ include $5$, $8$, $0$, $1$, and $2$.

Q: Can I use the inequality $x \leq -8$ to represent values that are greater than $-8$?

A: No, the inequality $x \leq -8$ cannot be used to represent values that are greater than $-8$. The inequality only represents values that are less than or equal to $-8$.

Q: Can I use the inequality $x \leq -8$ to represent values that are equal to $-8$?

A: Yes, the inequality $x \leq -8$ can be used to represent values that are equal to $-8$. Since $-8$ is less than or equal to $-8$, it satisfies the inequality.

Conclusion

In conclusion, the inequality $x \leq -8$ represents all values of $x$ that are less than or equal to $-8$. We hope this Q&A section has provided a clear understanding of the inequality and its representation. If you have any further questions or concerns, please don't hesitate to reach out.

Key Takeaways

• The inequality $x \leq -8$ represents all values of $x$ that are less than or equal to $-8$.
• Values that are greater than $-8$ do not satisfy the inequality $x \leq -8$.
• The inequality $x \leq -8$ can be used to represent values that are equal to $-8$.

Further Reading

If you are interested in learning more about inequalities and their representation, we recommend checking out the following resources:

• Khan Academy: Inequalities
• Mathway: Inequalities
• Wolfram MathWorld: Inequalities

We hope this article has provided a clear understanding of the inequality $x \leq -8$ and its representation. If you have any further questions or concerns, please don't hesitate to reach out.