let

x = the width of the rectangle

y = the length of the rectangle

a rectangle is 4 feet longer than its wide:

y = x + 4

the area of the rectangle must be less than or equal to 672 square feet:

x*y <= 672

plug y = x + 4 into the inequality:

x*(x + 4) <= 672

by solving we find:

-28<= x <= 24

click here to see the step by step solution of the inequality:

since x> 0

the possible values for the width x are in the interval (0 ,24].