Select The Correct Answer.Given The Following Formula, Solve For L L L . P = 2 ( L + B P=2(l+b P = 2 ( L + B ]A. L = 4 ( P + B \quad L=4(P+b L = 4 ( P + B ]B. L = P − B 4 \quad L=\frac{P-b}{4} L = 4 P − B ​ C. L = P − 2 B 2 \quad L=\frac{P-2b}{2} L = 2 P − 2 B ​ D. L = P − B 2 \quad L=\frac{P-b}{2} L = 2 P − B ​

Introduction

In this article, we will be solving for the variable $l$ in the given formula $P=2(l+b)$. This formula is a linear equation that involves two variables, $P$ and $l$, and a constant $b$. To solve for $l$, we need to isolate the variable $l$ on one side of the equation. We will use algebraic manipulations to solve for $l$.

Step 1: Isolate the Term with $l$

The first step in solving for $l$ is to isolate the term with $l$ on one side of the equation. We can do this by subtracting $2b$ from both sides of the equation.

P - 2b = 2l

Step 2: Divide Both Sides by 2

Next, we need to get rid of the coefficient 2 that is multiplying the variable $l$. We can do this by dividing both sides of the equation by 2.

\frac{P - 2b}{2} = l

Conclusion

Based on the steps above, we can see that the correct solution for $l$ is $\frac{P - 2b}{2}$. This is the solution that matches option C.

Discussion

Let's discuss the different options and why they are not correct.

• Option A: $\quad l=4(P+b)$

  This option is incorrect because it does not match the solution we derived. The correct solution has a coefficient of 1/2, not 4.

• Option B: $\quad l=\frac{P-b}{4}$

  This option is incorrect because it has a coefficient of 1/4, not 1/2. Additionally, the correct solution has a term of $-2b$, not $-b$.

• Option D: $\quad l=\frac{P-b}{2}$

  This option is incorrect because it has a term of $-b$, not $-2b$. Additionally, the correct solution has a coefficient of 1/2, not 1.

Conclusion

In conclusion, the correct solution for $l$ is $\frac{P - 2b}{2}$. This solution matches option C and is the only option that is correct.

Final Answer

The final answer is $\boxed{\frac{P - 2b}{2}}$.

References

• [1] Algebra textbook by Michael Artin
• [2] Online math resources by Khan Academy

Additional Resources

• [1] Mathway: A math problem solver
• [2] Wolfram Alpha: A computational knowledge engine

FAQs

• Q: What is the formula for solving for $l$? A: The formula is $l = \frac{P - 2b}{2}$.
• Q: Why is option A incorrect? A: Option A is incorrect because it has a coefficient of 4, not 1/2.
• Q: Why is option B incorrect? A: Option B is incorrect because it has a coefficient of 1/4, not 1/2, and a term of $-b$, not $-2b$.
• Q: Why is option D incorrect? A: Option D is incorrect because it has a term of $-b$, not $-2b$, and a coefficient of 1, not 1/2.
  Frequently Asked Questions (FAQs) =====================================

Q: What is the formula for solving for $l$?

A: The formula is $l = \frac{P - 2b}{2}$.

Q: Why is option A incorrect?

A: Option A is incorrect because it has a coefficient of 4, not 1/2. The correct solution has a coefficient of 1/2, which is derived from dividing both sides of the equation by 2.

Q: Why is option B incorrect?

A: Option B is incorrect because it has a coefficient of 1/4, not 1/2. Additionally, the correct solution has a term of $-2b$, not $-b$.

Q: Why is option D incorrect?

A: Option D is incorrect because it has a term of $-b$, not $-2b$. Additionally, the correct solution has a coefficient of 1/2, not 1.

Q: Can you explain the steps to solve for $l$?

A: Yes, the steps to solve for $l$ are as follows:

1. Isolate the term with $l$ on one side of the equation by subtracting $2b$ from both sides.
2. Divide both sides of the equation by 2 to get rid of the coefficient 2.

Q: What is the significance of the coefficient 1/2 in the correct solution?

A: The coefficient 1/2 is significant because it represents the ratio of $l$ to $P$. In other words, for every 1 unit of $P$, $l$ is 1/2 unit.

Q: Can you provide an example of how to use the formula to solve for $l$?

A: Yes, let's say we have the following values:

• $P = 10$
• $b = 2$

We can plug these values into the formula to solve for $l$:

$l = \frac{P - 2b}{2}$ $l = \frac{10 - 2(2)}{2}$ $l = \frac{10 - 4}{2}$ $l = \frac{6}{2}$ $l = 3$

Therefore, the value of $l$ is 3.

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

A: Some common mistakes to avoid when solving for $l$ include:

• Not isolating the term with $l$ on one side of the equation
• Not dividing both sides of the equation by 2 to get rid of the coefficient 2
• Using the wrong coefficient or term in the solution

Q: Can you recommend any resources for learning more about solving for $l$?

A: Yes, some recommended resources for learning more about solving for $l$ include:

• Algebra textbooks by Michael Artin
• Online math resources by Khan Academy
• Mathway: A math problem solver
• Wolfram Alpha: A computational knowledge engine

Conclusion

In conclusion, solving for $l$ in the given formula requires careful algebraic manipulations. By isolating the term with $l$ and dividing both sides of the equation by 2, we can derive the correct solution. We hope this article has been helpful in answering your questions and providing a better understanding of the topic.