For Which Of The Following Tables Are All The Values Of $x$ And Their Corresponding Values Of $y$ Solutions To The Inequality $2x - Y \ \textgreater \ 883$?A)$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$
Introduction
In mathematics, inequalities are used to describe relationships between variables. The given inequality, $2x - y \ \textgreater \ 883$, is a linear inequality that describes a region in the coordinate plane. In this article, we will explore which of the given tables satisfy this inequality.
Understanding the Inequality
The inequality $2x - y \ \textgreater \ 883$ can be rewritten as $y \ \textless \ 2x - 883$. This means that for any given value of $x$, the corresponding value of $y$ must be less than $2x - 883$ in order to satisfy the inequality.
Analyzing the Tables
We are given four tables, each with different values of $x$ and $y$. We need to determine which of these tables satisfy the inequality $2x - y \ \textgreater \ 883$.
Table A
| 400 | 800 |
| 500 | 900 |
| 600 | 1000 |
For each value of $x$ in Table A, we can calculate the corresponding value of $y$ that satisfies the inequality.
- For $x = 400$, $y \ \textless \ 2(400) - 883 = 817$, so $y$ can be 800.
- For $x = 500$, $y \ \textless \ 2(500) - 883 = 917$, so $y$ can be 900.
- For $x = 600$, $y \ \textless \ 2(600) - 883 = 1017$, so $y$ can be 1000.
Since all the values of $y$ in Table A satisfy the inequality, Table A is a solution to the inequality $2x - y \ \textgreater \ 883$.
Table B
| 400 | 900 |
| 500 | 1000 |
| 600 | 1100 |
For each value of $x$ in Table B, we can calculate the corresponding value of $y$ that satisfies the inequality.
- For $x = 400$, $y \ \textless \ 2(400) - 883 = 817$, so $y$ cannot be 900.
- For $x = 500$, $y \ \textless \ 2(500) - 883 = 917$, so $y$ cannot be 1000.
- For $x = 600$, $y \ \textless \ 2(600) - 883 = 1017$, so $y$ cannot be 1100.
Since not all the values of $y$ in Table B satisfy the inequality, Table B is not a solution to the inequality $2x - y \ \textgreater \ 883$.
Table C
| 400 | 700 |
| 500 | 800 |
| 600 | 900 |
For each value of $x$ in Table C, we can calculate the corresponding value of $y$ that satisfies the inequality.
- For $x = 400$, $y \ \textless \ 2(400) - 883 = 817$, so $y$ can be 700.
- For $x = 500$, $y \ \textless \ 2(500) - 883 = 917$, so $y$ can be 800.
- For $x = 600$, $y \ \textless \ 2(600) - 883 = 1017$, so $y$ can be 900.
Since all the values of $y$ in Table C satisfy the inequality, Table C is a solution to the inequality $2x - y \ \textgreater \ 883$.
Table D
| 400 | 1100 |
| 500 | 1200 |
| 600 | 1300 |
For each value of $x$ in Table D, we can calculate the corresponding value of $y$ that satisfies the inequality.
- For $x = 400$, $y \ \textless \ 2(400) - 883 = 817$, so $y$ cannot be 1100.
- For $x = 500$, $y \ \textless \ 2(500) - 883 = 917$, so $y$ cannot be 1200.
- For $x = 600$, $y \ \textless \ 2(600) - 883 = 1017$, so $y$ cannot be 1300.
Since not all the values of $y$ in Table D satisfy the inequality, Table D is not a solution to the inequality $2x - y \ \textgreater \ 883$.
Conclusion
In conclusion, only Table A and Table C satisfy the inequality $2x - y \ \textgreater \ 883$. This means that for any given value of $x$, the corresponding value of $y$ must be less than $2x - 883$ in order to satisfy the inequality.
Discussion
The inequality $2x - y \ \textgreater \ 883$ describes a region in the coordinate plane where the values of $x$ and $y$ satisfy the inequality. The tables provided in the problem are used to determine which values of $x$ and $y$ satisfy the inequality.
Final Answer
The final answer is Table A and Table C.
Introduction
In our previous article, we explored which of the given tables satisfy the inequality $2x - y \ \textgreater \ 883$. In this article, we will answer some frequently asked questions related to the problem.
Q1: What is the inequality $2x - y \ \textgreater \ 883$ used for?
A1: The inequality $2x - y \ \textgreater \ 883$ is used to describe a region in the coordinate plane where the values of $x$ and $y$ satisfy the inequality. It can be used in various mathematical and real-world applications, such as optimization problems, linear programming, and data analysis.
Q2: How do I determine which values of $x$ and $y$ satisfy the inequality?
A2: To determine which values of $x$ and $y$ satisfy the inequality, you can use the following steps:
- For each value of $x$, calculate the corresponding value of $y$ that satisfies the inequality.
- Check if the calculated value of $y$ is less than $2x - 883$.
- If the calculated value of $y$ is less than $2x - 883$, then the value of $x$ and $y$ satisfy the inequality.
Q3: What are the conditions for a table to be a solution to the inequality?
A3: A table is a solution to the inequality $2x - y \ \textgreater \ 883$ if all the values of $y$ in the table satisfy the inequality. In other words, for each value of $x$ in the table, the corresponding value of $y$ must be less than $2x - 883$.
Q4: Can a table have multiple solutions to the inequality?
A4: Yes, a table can have multiple solutions to the inequality. However, in the context of the problem, we are looking for tables that satisfy the inequality for all values of $x$ and $y$.
Q5: How do I know which tables satisfy the inequality?
A5: To determine which tables satisfy the inequality, you can use the following steps:
- For each table, calculate the corresponding value of $y$ that satisfies the inequality for each value of $x$.
- Check if all the calculated values of $y$ are less than $2x - 883$.
- If all the calculated values of $y$ are less than $2x - 883$, then the table is a solution to the inequality.
Q6: What are the implications of the inequality $2x - y \ \textgreater \ 883$?
A6: The inequality $2x - y \ \textgreater \ 883$ has various implications in mathematics and real-world applications. Some of the implications include:
- Optimization problems: The inequality can be used to optimize functions and find the maximum or minimum value of a function.
- Linear programming: The inequality can be used to solve linear programming problems and find the optimal solution.
- Data analysis: The inequality can be used to analyze data and find patterns and relationships between variables.
Q7: Can the inequality $2x - y \ \textgreater \ 883$ be used in other contexts?
A7: Yes, the inequality $2x - y \ \textgreater \ 883$ can be used in other contexts, such as:
- Economics: The inequality can be used to model economic systems and find the optimal solution to economic problems.
- Engineering: The inequality can be used to design and optimize systems and find the optimal solution to engineering problems.
- Computer science: The inequality can be used to solve problems in computer science, such as optimization problems and linear programming problems.
Conclusion
In conclusion, the inequality $2x - y \ \textgreater \ 883$ is a powerful tool that can be used in various mathematical and real-world applications. By understanding the inequality and its implications, we can solve problems and find the optimal solution to various problems.
Final Answer
The final answer is Table A and Table C.