To solve the equation \( P = 2l + 2w \) for \( l \), we want to isolate \( l \) on one side of the equation. Here are the steps:

1. Start with the original equation:

\[
P = 2l + 2w
\]

2. Subtract \( 2w \) from both sides to isolate terms with \( l \):

\[
P - 2w = 2l
\]

3. Divide both sides by 2 to solve for \( l \):

\[
l = \frac{P - 2w}{2}
\]

So, the solution for \( l \) is:

\[
l = \frac{P - 2w}{2}
\]

This expression gives the length \( l \) in terms of the perimeter \( P \) and width \( w \).

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Would you like more details on how this equation is used, or do you have any further questions? Here are some related questions:

1. How do you solve for \( w \) in the equation \( P = 2l + 2w \)?
2. What is the interpretation of \( P = 2l + 2w \) in geometry?
3. How does this formula relate to finding the perimeter of a rectangle?
4. What would happen if only \( P \) and \( l \) are known?
5. How would this formula change if dealing with the area of a rectangle instead?

**Tip:** When solving for a variable, remember to isolate it by performing inverse operations.

Learn how to solve the linear equation P = 2l + 2w for l with a clear step-by-step guide. This problem involves algebraic concepts such as isolating variables and rearranging equations. Perfect for students in Grades 6-8.

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