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

Understanding the Problem

In this problem, we are given two expressions representing the lengths of segments PR and RS in a geometric figure. We are asked to find the expression that represents the length of segment PS. To solve this problem, we need to use the given expressions to find the length of PS.

Given Expressions

• $PR = 4x - 2$
• $RS = 3x - 5$

Finding the Expression for PS

To find the expression for PS, we can use the fact that the sum of the lengths of segments PR and RS is equal to the length of segment PS. This is based on the concept of the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

However, in this case, we are not given a triangle, but rather two segments PR and RS. We can still use the concept of the triangle inequality to find the expression for PS. We can add the two given expressions and then simplify the result.

Step 1: Add the Given Expressions

We can add the two given expressions as follows:

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

Step 2: Simplify the Result

We can simplify the result by combining like terms:

$PR + RS = 7x - 7$

Conclusion

Based on the given expressions and the concept of the triangle inequality, we have found that the expression for PS is $7x - 7$. This is the correct answer.

Answer

The correct answer is C. $7x - 7$.

Explanation

The expression $7x - 7$ represents the length of segment PS. This expression is obtained by adding the given expressions for PR and RS and then simplifying the result.

Comparison with Other Options

We can compare our answer with the other options to see why they are incorrect. Option A is $x - 7$, which is not equal to $7x - 7$. Option B is $x - 3$, which is also not equal to $7x - 7$. Option D is $7x + 3$, which is not equal to $7x - 7$.

Conclusion

In conclusion, we have found that the expression for PS is $7x - 7$. This expression is obtained by adding the given expressions for PR and RS and then simplifying the result. We have also compared our answer with the other options to see why they are incorrect.

Final Answer

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Frequently Asked Questions

In this article, we will answer some frequently asked questions related to solving for PS in a geometric expression.

Q: What is the concept behind solving for PS?

A: The concept behind solving for PS is based on the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. However, in this case, we are not given a triangle, but rather two segments PR and RS. We can still use the concept of the triangle inequality to find the expression for PS.

Q: How do I add the given expressions for PR and RS?

A: To add the given expressions for PR and RS, we can simply combine like terms. For example, if we have the expressions $PR = 4x - 2$ and $RS = 3x - 5$, we can add them as follows:

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

Q: How do I simplify the result after adding the expressions?

A: To simplify the result after adding the expressions, we can combine like terms. For example, if we have the expression $PR + RS = 7x - 7$, we can simplify it by combining the like terms:

$PR + RS = 7x - 7$

Q: Why is the expression $7x - 7$ the correct answer?

A: The expression $7x - 7$ is the correct answer because it represents the length of segment PS. This expression is obtained by adding the given expressions for PR and RS and then simplifying the result.

Q: How do I compare my answer with the other options?

A: To compare your answer with the other options, you can simply substitute the values of x into each option and see which one equals the expression $7x - 7$. For example, if we have the options A, B, C, and D, we can substitute the value of x into each option as follows:

Option A: $x - 7$ Option B: $x - 3$ Option C: $7x - 7$ Option D: $7x + 3$

Q: Why are options A, B, and D incorrect?

A: Options A, B, and D are incorrect because they do not equal the expression $7x - 7$. For example, if we substitute the value of x into each option, we get:

Option A: $x - 7 \neq 7x - 7$ Option B: $x - 3 \neq 7x - 7$ Option D: $7x + 3 \neq 7x - 7$

Conclusion

In conclusion, we have answered some frequently asked questions related to solving for PS in a geometric expression. We have also provided examples and explanations to help you understand the concept behind solving for PS.

Final Answer

The final answer is C. $7x - 7$.

Additional Resources

If you have any additional questions or need further clarification, please refer to the following resources:

• Geometric Expressions
• Triangle Inequality
• Algebraic Expressions

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