How to respond to "solve this equation" in a basic algebra class

Solution 1:

To put it bluntly, those of your colleagues who don’t accept ‘$x=1$’ as a solution don’t speak English. That sort of hyperpedantry accomplishes nothing beyond making students think that mathematics is all about invoking the right (incomprehensible) magic formula(s). I’ll go so far as to say that I think it excessive pedantry to object to $x=\frac12\left(1\pm\sqrt5\right)$ as an answer to a question asking for the solution(s) to $x^2-x-1=0$.

It would be another matter if the question were written The solution set is __: that question clearly calls for a set. In that case, however, the script should accept $\{1\}$, $\{x\in\Bbb R:x=1\}$, $\{x:x=1\}$, $[1,1]$, and any other reasonably straightforward variant, but not $x=1$, $1$, or the like.

Solution 2:

If they are happy with "The solution set is $\{x\mid x=1\}$", they should also be happy with $\{x\mid 2x+3=6-x\}$" which is equivalent.

If the above $x=1$ answer is not acceptable for some of your collegues, but many students are doing it as I guess it's happening, they should first think about what they did wrong: in this case write a question stating clearly that they want the student performing two tasks. Putting the equation in some canonical form with the variable isolated on the left side, secondly states that they know that the result is a set. Outside pedantic mathematic, the second part is irrelevant, and it is disputable that may even be seen as a secondary goal of the exercise.

Which student could believe a corrector is so dumb the corrector may ignore that the result is a set ? If The result is say $x = 11$, should the student also state that he is using base 10 arithmetic ? If the base could possibly be binary it could be ambiguous.