To solve this problem, we first need to understand the problem statement correctly. We have given the formula for the perimeter (P) of a rectangle which is P = 2l + 2w, where l and w are the length and width of the rectangle, respectively. We are required to solve this equation for w, i.e., express w in terms of P and l.
Let's start with the given formula:
P = 2l + 2w
Our goal is to isolate w on one side of the equation. First, we subtract 2l from both sides of the equation:
P - 2l = 2w
We are close to our answer, we just need to get only w on one side. As we see, w is currently multiplied by 2, so we divide both sides of the equation by 2 to solve for w:
w = (P - 2l)/2
So, the correct expression is "w = (P - 2l)/2", which matches with option d.
Therefore, the correct answer is "option d: w = (P - 2l)/2".