To find what x is equal to, simply isolate it, that is, put any x terms on one side of the equation, and the remaning things you'll put on the opposite side of the equation.
The reason why you would subtract 7 from both sides is because it leads to isolating the x-variable. The reason why you DON'T add seven to both sides of the equation is because you won't isolate the x-variable. By adding 7 to both sides, you'll get . We want to know what x is, not what is.
EDIT: As a side note, equations are alive! They say things in natural language. If you have the equation , this is saying that IS , and that IS . Similarly, if you have the equation , this is saying that IS , and that IS