math alegbra 9th grade ny regents

Question

students were asked to write a formula for the length of a rectangle by using the formula for its perimeter, p=2l+2w.. three of their responses are shown below

1. l= 1/2(p) -w
2. 1/2(p-2w)
3. p-2w/2

which are correct?

Answer 1

1 is the correct answer because it is complete with the equal sign

Since

p = 2l + 2w

Stepwise

You can start by factoring out 2 on one side of the equation to give

p= 2(l + w)

Next divide both sides of the equation by 2 to give

p/2 = l + w

Then to solve for the length, l, subtract w from both sides of the equation to give

p/2 - w = 1/2(p) - w = l

Answer selection 1 is complete with the equal sign

Answer selection 2 is not set equal to anything, however once put in simplest terms, by distributing the 1/2 through the parentheses, is equal to selection 1.

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