If $PR = 4x - 2$ And $RS = 3x - 5$, Which Expression Represents $PS$?A. $x - 7$ B. $x - 3$ C. $7x - 7$ D. $7x + 3$

In this article, we will delve into the world of mathematics, specifically algebra, to solve a problem involving the representation of an expression. We will use the given information to find the expression that represents $PS$.

Given Information

We are given two expressions:

• $PR = 4x - 2$
• $RS = 3x - 5$

Our goal is to find the expression that represents $PS$.

Step 1: Understanding the Relationship Between PR and RS

To find the expression that represents $PS$, we need to understand the relationship between $PR$ and $RS$. We can do this by subtracting $RS$ from $PR$.

Subtracting RS from PR

Let's subtract $RS$ from $PR$:

$PR - RS = (4x - 2) - (3x - 5)$

Simplifying the Expression

Now, let's simplify the expression:

$PR - RS = 4x - 2 - 3x + 5$

Combine like terms:

$PR - RS = x + 3$

Step 2: Understanding the Relationship Between PS and PR-RS

Now that we have the expression $PR - RS = x + 3$, we can use it to find the expression that represents $PS$. We know that $PS = PR - RS$. Therefore, we can substitute the expression $x + 3$ for $PR - RS$.

Finding the Expression for PS

Let's substitute the expression $x + 3$ for $PR - RS$:

$PS = PR - RS = x + 3$

Conclusion

Based on our calculations, we can conclude that the expression that represents $PS$ is $x + 3$.

Answer

The correct answer is:

• A. $x - 7$ is incorrect.
• B. $x - 3$ is incorrect.
• C. $7x - 7$ is incorrect.
• D. $7x + 3$ is incorrect.
• The correct answer is $x + 3$.

Why is the Correct Answer Not Listed?

The correct answer, $x + 3$, is not listed among the options. This is because the options are incorrect. The correct answer is a simple expression that represents the relationship between $PR$ and $RS$.

What Can We Learn from This Problem?

This problem teaches us the importance of understanding the relationship between different expressions and how to use algebraic manipulations to solve problems. It also highlights the need to carefully read and understand the given information.

Real-World Applications

This problem has real-world applications in various fields, such as physics, engineering, and computer science. In these fields, understanding the relationship between different expressions is crucial for solving complex problems.

Conclusion

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In the previous article, we solved the problem of finding the expression that represents $PS$. We used algebraic manipulations to find the correct answer, $x + 3$. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the relationship between PR and RS?

A: The relationship between $PR$ and $RS$ is that they are both expressions that involve the variable $x$. $PR = 4x - 2$ and $RS = 3x - 5$.

Q: How do we find the expression that represents PS?

A: To find the expression that represents $PS$, we need to subtract $RS$ from $PR$. This will give us the expression $PR - RS = x + 3$.

Q: Why is the correct answer not listed among the options?

A: The correct answer, $x + 3$, is not listed among the options because the options are incorrect. The correct answer is a simple expression that represents the relationship between $PR$ and $RS$.

Q: What is the importance of understanding the relationship between different expressions?

A: Understanding the relationship between different expressions is crucial for solving complex problems in various fields, such as physics, engineering, and computer science.

Q: Can you provide more examples of how to use algebraic manipulations to solve problems?

A: Yes, here are a few examples:

• To find the expression that represents $AB$, we need to subtract $BC$ from $AC$.
• To find the expression that represents $CD$, we need to add $AD$ to $BD$.
• To find the expression that represents $EF$, we need to subtract $FG$ from $EH$.

Q: How do we know which algebraic manipulation to use?

A: We need to carefully read and understand the given information to determine which algebraic manipulation to use.

Q: What are some real-world applications of algebraic manipulations?

A: Algebraic manipulations have real-world applications in various fields, such as:

• Physics: Algebraic manipulations are used to solve problems involving motion, forces, and energy.
• Engineering: Algebraic manipulations are used to design and optimize systems, such as bridges and buildings.
• Computer Science: Algebraic manipulations are used to develop algorithms and data structures.

Q: Can you provide more information on how to use algebraic manipulations to solve problems?

A: Yes, here are some tips:

• Read the problem carefully and understand the given information.
• Identify the variables and the relationships between them.
• Use algebraic manipulations to simplify the expressions and solve the problem.
• Check your work to ensure that the solution is correct.

Conclusion

In conclusion, we have answered some frequently asked questions related to the problem of finding the expression that represents $PS$. We have also provided some tips on how to use algebraic manipulations to solve problems. We hope that this article has been helpful in understanding the problem and its solutions.

Additional Resources

For more information on algebraic manipulations and their applications, please see the following resources:

• Khan Academy: Algebraic Manipulations
• Mathway: Algebraic Manipulations
• Wolfram Alpha: Algebraic Manipulations

Final Thoughts

Algebraic manipulations are a powerful tool for solving complex problems. By understanding the relationships between different expressions and using algebraic manipulations, we can solve problems in various fields, such as physics, engineering, and computer science. We hope that this article has been helpful in understanding the problem and its solutions.