The formula for the perimeter of a rectangle can be expressed in more than one way. One way is P=2(l + w). Discuss how you could manipulate this equation to isolate l. Write down the steps and include and explanation of each step. Is there more than one way to do this? Explain

To isolate l (the length of the rectangle) in the perimeter formula P = 2(l + w), you need to perform algebraic operations that will get l by itself on one side of the equation. Here are the steps to do that:

Step 1: Start with the formula for the perimeter of a rectangle: P = 2(l + w)

Step 2: Divide both sides of the equation by 2 to undo the multiplication by 2 on the right-hand side. This step will give us the sum of the length and width: P / 2 = (2(l + w)) / 2

Step 3: Simplify the right side of the equation. Since (2(l + w)) / 2 is the same as 2/2 * (l + w), and 2/2 is equal to 1, we simply get: P / 2 = l + w

Step 4: To isolate l, you need to subtract w from both sides of the equation. This step removes w from the right side because w - w equals zero: (P / 2) - w = l + w - w

Step 5: Simplify the equation by combining like terms on the right-side: (P / 2) - w = l

Now, l is isolated on one side of the equation, and the equation is solved for l: l = (P / 2) - w

Extra: The perimeter of a rectangle is the total distance around the outside of the rectangle. It is calculated by adding together the lengths of all four sides. Since a rectangle has two pairs of equal sides (opposite sides are equal), you can calculate the perimeter by adding the length (l) and the width (w) and then multiplying by 2, because there are two lengths and two widths.

There is more than one way to isolate l in the equation P = 2(l + w). You can also start by expanding the equation first and then divide P by 2, which will lead you to the same result:

P = 2l + 2w (by distributing the 2 to both l and w) P - 2w = 2l (by subtracting 2w from both sides) (P - 2w) / 2 = l (then by dividing both sides by 2)

Both methods lead to the same expression for l, showing that l (the length) can be found by taking half the perimeter and subtracting the width. Understanding how to manipulate equations is an important part of algebra, which helps us solve for unknown variables.