Arectangular house measuring 50 feet by 24 feet is to have a gravel pathway of constant width built all around it. there is enough gravel to cover 345 square feet or less. create an inequality that represents all possible widths (w), in feet, of the pathway

First, we determine the area of the rectangular house by multiplying the length by the width. That is,
             area of the house = (50 ft)(24 ft) = 1200 ft²
Given that all sides of the house should have the pathway, the length of the house plus the pathway should be 50+2x and the new width would be 24+2x. The new area minus the original area of the house should not be more than 345 ft². Thus, the equation would be,
                                   (50+2x)(24+2x) - 1200 ≤ 345