literal equation

Question

The formula for the perimeter of a rectangle is P=2(l+w).

Part A. Rewrite the formula for the perimeter of a rectangle in terms of the width, w. In your final answer, include all of your work.

Part B. In two or more complete sentences, describe the process you followed while isolating the variable w in the equation P=2(l+w).

Answer 1

The question really is, REWRITE THE FOLLOWING EQUATION IN TERMS OF W, OR SOLVE FOR W.

That means getting W by itself on the left or right side of the equation BY ITSELF. That's what "ISOLATING THE VARIABLE" means.

We are given the equation:

P = 2(L + W)

Step 1: Distribute the 2(L + W)

P = 2L + 2W

Step 2: Subtract 2L from both sides of the equation.

P - 2L = 2L - 2L + 2W

P - 2L = 0 + 2W

P - 2L = 2W

Step 3: Divide by 2 on both sides of the equation:

P - 2L 2W

-------- = --------

2 2

P - 2L

-------- = W (The 2's cancel each other.)

2

P - 2L

W = --------- (Reversed the equation.)

2

END OF PART A.

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PART B.

Part B. In two or more complete sentences, describe the process you followed while isolating the variable w in the equation P=2(l+w).

I used the distributive property to expand the right side of the equation. Then, I subtracted 2L from both sides of the equation, leaving 2W by itself on the right. The last step was dividing both sides of the equation by two, so the two's would cancel each other out, and I had W alone, by itself, or isolated.