x represents the ideal weight of the dog. The first equation is correct because the ideal weight increased by seven pounds equals 44, since he currently weighs 44 pounds and must decrease that by 7 to get the ideal weight. The second one is also correct because 44 minus the ideal weight is seven, since seven is given as the difference between 44 and the ideal weight.
Another equation would be x=44-7. This is because the ideal weight is 44 pounds minus the seven pounds the dog loses.
