The perimeter of a rectangle is 16 inches. the equation that represents the perimeter of the rectangle is 2l + 2w = 16, where l represents the length of the rectangle and w represents the width of the rectangle. which value is possible for the length of the rectangle?

Let's start with the formula for the perimeter of a rectangle of length L and width W:  P = 2W + 2L.  We are told that this perimeter is 16.  What is the length, L, of the rectangle?

Solving 16 = 2W + 2L for L:
 
                                       2L = 16 - 2W, or L = 8 - W

Important:  since L cannot be negative, W must be 8 or smaller, but not negative or zero.
Checks:  If W=8, L = 8 - 8 = 0    This is reasonable.
               If W is just barely greater than 0, L = 8 - 0+, or approx. 8.  This is reasonable also.

 0<L<8