Hm, maybe the author wants to confuse his students as much as he can, for whatever reason (maybe he has a trauma and hates students or is simply evil?). The standard reading is that x+4=7 is an equation with one unknown to be solved. There are three possibilities: (i) it has at least one solution, (ii) it has no solution, (iii) it is undecidable within the used set of axioms. In case (i) you may have two subcases (ia) there's a unique solution, (iib) there is more then one distinct solution. In this case, interpreting as ##x## standing for any real number we know that this is linear equation with one unknown, which has a unique solution, and indeed subtracting 4 on both sides of the equation tells you that without other possibility you must have x=3. So there's exactly one solution of the equation. Of course, putting for x any other number than 3 leads to a wrong equation.