The Point $(0,0)$ Is A Solution To Which Of These Inequalities?A. Y + 5 \textless 3 X + 4 Y + 5 \ \textless \ 3x + 4 Y + 5 \textless 3 X + 4 B. Y − 4 \textless 3 X − 5 Y - 4 \ \textless \ 3x - 5 Y − 4 \textless 3 X − 5 C. Y − 5 \textless 3 X − 4 Y - 5 \ \textless \ 3x - 4 Y − 5 \textless 3 X − 4 D. Y + 5 \textless 3 X − 4 Y + 5 \ \textless \ 3x - 4 Y + 5 \textless 3 X − 4

Introduction

In mathematics, inequalities are a fundamental concept used to describe relationships between variables. They are used to express the idea that one quantity is greater than, less than, or equal to another quantity. In this article, we will explore the concept of inequalities and determine which of the given inequalities has the point (0,0) as a solution.

Understanding Inequalities

An inequality is a statement that compares two expressions and indicates whether one is greater than, less than, or equal to the other. Inequalities can be written in various forms, including:

• Greater than: a > b
• Less than: a < b
• Greater than or equal to: a ≥ b
• Less than or equal to: a ≤ b

The Point (0,0) and Inequalities

To determine which of the given inequalities has the point (0,0) as a solution, we need to substitute the values of x and y into each inequality and evaluate the result.

A. $y + 5 \ \textless \ 3x + 4$

To determine if the point (0,0) is a solution to this inequality, we substitute x = 0 and y = 0 into the inequality:

$0 + 5 \ \textless \ 3(0) + 4$

Simplifying the inequality, we get:

$5 \ \textless \ 4$

This is a false statement, as 5 is not less than 4. Therefore, the point (0,0) is not a solution to this inequality.

B. $y - 4 \ \textless \ 3x - 5$

To determine if the point (0,0) is a solution to this inequality, we substitute x = 0 and y = 0 into the inequality:

$0 - 4 \ \textless \ 3(0) - 5$

Simplifying the inequality, we get:

$-4 \ \textless \ -5$

This is a false statement, as -4 is not less than -5. Therefore, the point (0,0) is not a solution to this inequality.

C. $y - 5 \ \textless \ 3x - 4$

To determine if the point (0,0) is a solution to this inequality, we substitute x = 0 and y = 0 into the inequality:

$0 - 5 \ \textless \ 3(0) - 4$

Simplifying the inequality, we get:

$-5 \ \textless \ -4$

This is a true statement, as -5 is indeed less than -4. Therefore, the point (0,0) is a solution to this inequality.

D. $y + 5 \ \textless \ 3x - 4$

To determine if the point (0,0) is a solution to this inequality, we substitute x = 0 and y = 0 into the inequality:

$0 + 5 \ \textless \ 3(0) - 4$

Simplifying the inequality, we get:

$5 \ \textless \ -4$

This is a false statement, as 5 is not less than -4. Therefore, the point (0,0) is not a solution to this inequality.

Conclusion

In conclusion, the point (0,0) is a solution to the inequality $y - 5 \ \textless \ 3x - 4$. This is because when we substitute x = 0 and y = 0 into the inequality, we get a true statement. The other inequalities do not have the point (0,0) as a solution, as they result in false statements when we substitute the values of x and y.

Key Takeaways

• Inequalities are used to describe relationships between variables.
• The point (0,0) is a solution to the inequality $y - 5 \ \textless \ 3x - 4$.
• The other inequalities do not have the point (0,0) as a solution.

Further Reading

For further reading on inequalities and mathematical analysis, we recommend the following resources:

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

Introduction

In our previous article, we explored the concept of inequalities and determined which of the given inequalities has the point (0,0) as a solution. In this article, we will provide a Q&A guide to help you better understand the concept of inequalities and how to analyze them.

Q&A Guide

Q: What is an inequality?

A: An inequality is a statement that compares two expressions and indicates whether one is greater than, less than, or equal to the other.

Q: What are the different types of inequalities?

A: There are four main types of inequalities:

• Greater than: a > b
• Less than: a < b
• Greater than or equal to: a ≥ b
• Less than or equal to: a ≤ b

Q: How do I determine if a point is a solution to an inequality?

A: To determine if a point is a solution to an inequality, you need to substitute the values of x and y into the inequality and evaluate the result.

Q: What is the point (0,0) and why is it important?

A: The point (0,0) is a special point in mathematics that represents the origin of a coordinate plane. It is important because it is often used as a reference point in mathematical equations and inequalities.

Q: Which inequality has the point (0,0) as a solution?

A: The inequality $y - 5 \ \textless \ 3x - 4$ has the point (0,0) as a solution.

Q: Why is it important to understand inequalities?

A: Understanding inequalities is important because it helps you to analyze and solve mathematical problems. Inequalities are used to describe relationships between variables, and they are a fundamental concept in mathematics.

Q: What are some real-world applications of inequalities?

A: Inequalities have many real-world applications, including:

• Finance: Inequalities are used to calculate interest rates and investment returns.
• Science: Inequalities are used to describe the relationships between variables in scientific experiments.
• Engineering: Inequalities are used to design and optimize systems.

Q: How can I practice solving inequalities?

A: You can practice solving inequalities by working through examples and exercises in your textbook or online resources. You can also try solving inequalities on your own by substituting values into the inequality and evaluating the result.

Conclusion

In conclusion, understanding inequalities is an important concept in mathematics that has many real-world applications. By practicing solving inequalities, you can develop a deeper understanding of mathematical relationships and solve problems with confidence.

Key Takeaways

• Inequalities are used to describe relationships between variables.
• The point (0,0) is a solution to the inequality $y - 5 \ \textless \ 3x - 4$.
• Inequalities have many real-world applications.
• Practicing solving inequalities can help you develop a deeper understanding of mathematical relationships.

Further Reading

For further reading on inequalities and mathematical analysis, we recommend the following resources:

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

By understanding the concept of inequalities and how to analyze them, you can develop a deeper understanding of mathematical relationships and solve problems with confidence.