Sure, let's solve the given equation step by step to find an equivalent equation for \(w\).
We start with the equation for the perimeter \(P\) of a rectangle, given by:
[tex]\[ P = 2(l + w) \][/tex]
Our goal is to solve for \(w\).
1. Isolate the term containing \(w\):
To isolate \(w\), we first need to simplify the equation by getting rid of the 2 that multiplies the expression inside the parentheses:
[tex]\[ \frac{P}{2} = l + w \][/tex]
2. Solve for \(w\):
Now we need to isolate \(w\). To do this, subtract \(l\) from both sides of the equation:
[tex]\[ \frac{P}{2} - l = w \][/tex]
3. Simplify the equation:
To look similar to the given options, let's combine the terms on the right side of the equation:
[tex]\[ w = \frac{P}{2} - l \][/tex]
To present it in the form that may match the provided options, we need to have a common denominator when combining the terms \(\frac{P}{2}\) and \(-l\).
[tex]\[ w = \frac{P}{2} - \frac{2l}{2} \][/tex]
4. Combine the fractions:
Combine the terms into a single fraction:
[tex]\[ w = \frac{P - 2l}{2} \][/tex]
So, the equation equivalent to \( P = 2(l + w) \) is:
[tex]\[ w = \frac{P - 2l}{2} \][/tex]
Looking at the provided options:
1. \( w = P - 2l \)
2. \( w = P - 1 \)
3. \( w = \frac{P - 2l}{2} \)
4. \( w = \frac{P + 2l}{2} \)
The equation \( w = \frac{P - 2l}{2} \) matches the third option.
Thus, the correct answer is:
[tex]\[ \boxed{3} \][/tex]
