Finding the Expression for PS

Oct 13, 2025 by windailys.com 67 views

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 and apply basic algebraic operations to find the desired expression.

Given Expressions

We are given two 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. Mathematically, this can be represented as:

$PR + RS = PS$

Substituting the given expressions for PR and RS, we get:

$(4x - 2) + (3x - 5) = PS$

Simplifying the Expression

To simplify the expression, we can combine like terms:

$7x - 7 = PS$

Comparing with the Options

Now that we have found the expression for PS, we can compare it with the given options:

A. $x - 7$
B. $x - 3$
C. $7x - 7$
D. $7x + 3$

Conclusion

Based on our calculations, we can see that the expression for PS is $7x - 7$ . Therefore, the correct answer is:

C. $7x - 7$

This expression represents the length of segment PS in terms of the variable x.

Step-by-Step Solution

Here's a step-by-step solution to the problem:

Given Expressions: We are given two expressions representing the lengths of segments PR and RS.
Finding the Expression for PS: We use the fact that the sum of the lengths of segments PR and RS is equal to the length of segment PS.
Simplifying the Expression: We combine like terms to simplify the expression.
Comparing with the Options: We compare the simplified expression with the given options to find the correct answer.

Key Concepts

Geometric Expressions: We use geometric expressions to represent the lengths of segments in a geometric figure.
Algebraic Operations: We apply basic algebraic operations, such as addition and combination of like terms, to simplify the expression.
Comparison with Options: We compare the simplified expression with the given options to find the correct answer.

Real-World Applications

This problem has real-world applications in various fields, such as:

Geometry: We use geometric expressions to represent the lengths of segments in geometric figures.
Algebra: We apply algebraic operations to simplify expressions and solve equations.
Engineering: We use geometric expressions to represent the lengths of segments in engineering applications, such as building design and construction.

Conclusion

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 formula for finding PS?

A: The formula for finding PS is:

$PR + RS = PS$

This formula represents the sum of the lengths of segments PR and RS, which is equal to the length of segment PS.

Q: How do I simplify the expression for PS?

A: To simplify the expression for PS, you can combine like terms. For example, if you have the expression:

$(4x - 2) + (3x - 5)$

You can simplify it by combining the like terms:

$7x - 7$

Q: What is the correct answer for PS?

A: The correct answer for PS is:

$7x - 7$

This expression represents the length of segment PS in terms of the variable x.

Q: Can I use this formula for other geometric expressions?

A: Yes, you can use this formula for other geometric expressions. The formula is a general rule that applies to any geometric figure with segments PR and RS.

Q: What are some real-world applications of this formula?

A: Some real-world applications of this formula include:

Geometry: You can use this formula to find the length of segments in geometric figures.
Algebra: You can use this formula to simplify expressions and solve equations.
Engineering: You can use this formula to find the length of segments in engineering applications, such as building design and construction.

Q: How do I know which option is correct?

A: To know which option is correct, you can compare the simplified expression with the given options. In this case, the correct answer is:

C. $7x - 7$

Q: Can I use this formula for expressions with different variables?

A: Yes, you can use this formula for expressions with different variables. The formula is a general rule that applies to any geometric figure with segments PR and RS, regardless of the variables used.

Q: What are some common mistakes to avoid when solving for PS?

A: Some common mistakes to avoid when solving for PS include:

Not combining like terms: Make sure to combine like terms to simplify the expression.
Not comparing with options: Make sure to compare the simplified expression with the given options to find the correct answer.
Not using the correct formula: Make sure to use the correct formula to find the length of segment PS.

Conclusion

In conclusion, we have answered some frequently asked questions related to solving for PS in a geometric expression. We have provided the formula for finding PS, simplified the expression, and compared it with the given options to find the correct answer. We have also discussed some real-world applications of this formula and common mistakes to avoid when solving for PS.