I will remark, in some horror and exasperation with the modern educational system, that I do not recall any math-book of my youth ever once explaining that the reason why you are always allowed to add 1 to both sides of an equation is that it is a kind of step which always produces true equations from true equations.

Would the average 9-year old be able to understand such a math book? (For that matter, would the average teacher of 9-year-olds?)