Marisol is making a rectangular wooden frame. she wants the length of the frame to be no more than 12 inches. she has less than 30 inches of wood to use. which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?
l ≤ 12
2l + 2w < 30
l > 12
2l + 2w < 30
l ≤ 12
l + w < 30
l > 12
l + w < 30

For this case, the first thing we must do is define variables.
 We have then:
 w: width of wooden frame
 l: length of the wooden frame.
 We now write the system of equations:
 She wants the length of the frame to be no more than 12 inches:
 l ≤ 12
 She has less than 30 inches of wood to use. Therefore, the perimeter of the frame is given by:
 2w + 2l <30
 
 A system of inequalities that represents the possible length, and the possible width, that her frame could have is:
 l ≤ 12
 2l + 2w <30

A rectangle is made up of 2 sets of equivalent sides... 2 lengths and 2 widths.  We know that the length is "no more" than 12 inches, so the length is  ≤ 12.  We also know that she has "less than" 30 inches of wood, so she has < 30 inches.

The only system of inequalities that meets all of these is

l ≤ 12
2l + 2w < 30

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