Arectangle has a length of 22 inches less than 7 times its width. if the area of the rectangle is 3197 square inches, find the length of the rectangle.

The area formula for a rectangle is A = L*W.  We have the area as 3197, now we just have to find a way to directly relate the length to the width with only one unknown, since we can't have 2 unknowns.  The problem tells us that the length is 22 in. less than 7xW.  That will be expressed as L=7W-22, and width is just W.  Filling in we have 3197=W(7W-22).  Distributing through the parenthesis we have . Since we have to solve for x and the only way we can do that is by factoring, we will move the 3197 over to the other side by subtraction and then factor the quadratic.  .  I recommend putting that into the quadratic formula, and when you do you get W values of 23 and -19.857  The only 2 things in math that will never EVER be negative are time and distance/length.  And since one of our lengths there is negative we know that that is not the one we will use.  Therefore, the width is 23.  The length then is L=7(23)-22 which is 139