Which Compound Inequality Represents The Length, $w$, Of Kylie's Essay?A. $500 \leq W \leq 150$B. $150 \geq W$C. $500 \leq W$D. $150 \leq W \leq 500$

Introduction

In mathematics, inequalities are used to represent a relationship between two values. A compound inequality is a combination of two or more inequalities that are connected by logical operators such as "and" or "or." In this article, we will explore the concept of compound inequalities and use it to determine the length of Kylie's essay.

What is a Compound Inequality?

A compound inequality is a mathematical statement that combines two or more inequalities using logical operators. It is used to represent a range of values that satisfy multiple conditions. For example, the compound inequality $2 \leq x \leq 5$ represents a range of values from 2 to 5, inclusive.

Types of Compound Inequalities

There are two main types of compound inequalities: conjunction and disjunction.

• Conjunction: A conjunction is a compound inequality that combines two or more inequalities using the logical operator "and." For example, the compound inequality $2 \leq x \leq 5$ and $x > 3$ represents a range of values that satisfy both conditions.
• Disjunction: A disjunction is a compound inequality that combines two or more inequalities using the logical operator "or." For example, the compound inequality $2 \leq x \leq 5$ or $x > 7$ represents a range of values that satisfy either condition.

Understanding the Problem

Kylie's essay has a minimum length of 150 words and a maximum length of 500 words. We need to determine which compound inequality represents the length of Kylie's essay.

Analyzing the Options

Let's analyze each option:

• Option A: $500 \leq w \leq 150$. This option is incorrect because the minimum length is 150 words, and the maximum length is 500 words. The compound inequality is also incorrect because it is in the wrong order.
• Option B: $150 \geq w$. This option is incorrect because it only represents the minimum length of 150 words and does not include the maximum length of 500 words.
• Option C: $500 \leq w$. This option is incorrect because it only represents the maximum length of 500 words and does not include the minimum length of 150 words.
• Option D: $150 \leq w \leq 500$. This option is correct because it represents the minimum length of 150 words and the maximum length of 500 words.

Conclusion

In conclusion, the compound inequality that represents the length of Kylie's essay is $150 \leq w \leq 500$. This option correctly represents the minimum length of 150 words and the maximum length of 500 words.

Key Takeaways

• A compound inequality is a combination of two or more inequalities that are connected by logical operators.
• There are two main types of compound inequalities: conjunction and disjunction.
• A compound inequality can be used to represent a range of values that satisfy multiple conditions.
• When analyzing a compound inequality, it is essential to consider the logical operators used to connect the inequalities.

Final Thoughts

In this article, we explored the concept of compound inequalities and used it to determine the length of Kylie's essay. We analyzed each option and determined that the correct compound inequality is $150 \leq w \leq 500$. This option correctly represents the minimum length of 150 words and the maximum length of 500 words.

Introduction

In our previous article, we explored the concept of compound inequalities and used it to determine the length of Kylie's essay. In this article, we will answer some frequently asked questions about compound inequalities.

Q: What is a compound inequality?

A: A compound inequality is a combination of two or more inequalities that are connected by logical operators such as "and" or "or." It is used to represent a range of values that satisfy multiple conditions.

Q: What are the two main types of compound inequalities?

A: The two main types of compound inequalities are conjunction and disjunction.

• Conjunction: A conjunction is a compound inequality that combines two or more inequalities using the logical operator "and." For example, the compound inequality $2 \leq x \leq 5$ and $x > 3$ represents a range of values that satisfy both conditions.
• Disjunction: A disjunction is a compound inequality that combines two or more inequalities using the logical operator "or." For example, the compound inequality $2 \leq x \leq 5$ or $x > 7$ represents a range of values that satisfy either condition.

Q: How do I determine the correct compound inequality?

A: To determine the correct compound inequality, you need to analyze the problem and identify the minimum and maximum values. Then, you can use the logical operators "and" or "or" to connect the inequalities.

Q: What is the difference between a compound inequality and a single inequality?

A: A single inequality represents a single value or a range of values, while a compound inequality represents a range of values that satisfy multiple conditions.

Q: Can a compound inequality have more than two inequalities?

A: Yes, a compound inequality can have more than two inequalities. For example, the compound inequality $2 \leq x \leq 5$ and $x > 3$ and $x < 10$ represents a range of values that satisfy all three conditions.

Q: How do I solve a compound inequality?

A: To solve a compound inequality, you need to analyze the logical operators used to connect the inequalities. If the logical operator is "and," you need to find the intersection of the two inequalities. If the logical operator is "or," you need to find the union of the two inequalities.

Q: Can a compound inequality have negative values?

A: Yes, a compound inequality can have negative values. For example, the compound inequality $-5 \leq x \leq 5$ represents a range of values that include negative values.

Q: How do I graph a compound inequality?

A: To graph a compound inequality, you need to graph each inequality separately and then combine the graphs using the logical operators "and" or "or."

Conclusion

In conclusion, compound inequalities are a powerful tool for representing a range of values that satisfy multiple conditions. By understanding the concept of compound inequalities and how to analyze and solve them, you can apply this knowledge to a wide range of problems in mathematics and real-life situations.

Key Takeaways

• A compound inequality is a combination of two or more inequalities that are connected by logical operators.
• There are two main types of compound inequalities: conjunction and disjunction.
• A compound inequality can be used to represent a range of values that satisfy multiple conditions.
• When analyzing a compound inequality, it is essential to consider the logical operators used to connect the inequalities.

Final Thoughts

In this article, we answered some frequently asked questions about compound inequalities. We hope that this article has provided you with a better understanding of compound inequalities and how to apply this knowledge to real-life situations.