Which of the following equations has the solution set {0}?

The correct answer is:  

          [A]:  " -14m − 7m + 1  =  -7m + 1 " .

Note:  All of the answer choices given contain "ONE" variable, "m". 

            Among the all the answer choices given (that is, among all the 3 (THREE) answer choices given),  this answer choice: "{A}", is the only one which holds true; (that is, maintains a true equation— both sides of the equation are equal—, when "m = 0 ").

Specifically, for "Answer choice: [A]:

    -14m − 7m + 1 =  -7m + 1 ; 

When we plug in "0" for all values of "m", both sides of the equation are equal:

   -14*(0)  −  7*(0) + 1  =?   -7*(0)  +  1  ?? ;

        0  − 0  + 1 = ?   0 + 1 ?

                    1 = 1 ?  Yes!

Let's try Answer choice: [B] ; which is:

     "-14m + 7m + 1  =  -7m + 2 " ;

 If we plug in "0" for ALL values of "m" (both sides, of course), does the equation hold true?

     -14*(0) + 7*(0) + 1  = ?   -7*(0)  + 2  ?? ;

              0 + 0 + 1 = ?   0 + 2 ?? ; 

                         1 = ?   2 ???   No!    1 ≠ 2 ; 

           As such, "Answer choice: [B}" does NOT have the solution set:  "{0}" ; and is not the correct answer; (and is not a correct answer).

Now, let's try the remaining  "Answer choice:  [C]:"

    14m −  7m − 1  =  -7m + 1 ; 

 If we plug in "0" for ALL values of "m" (both sides, of course), does the equation hold true? 

    14*(0)  −  7*(0)  −  1  =  -7*(0)  +  1 ;

     0  − 0  − 1  =?   0 + 1 ?? ;

              - 1  = ?  1 ???  No!    -1  ≠  1 !   ; 

         As such, "Answer choice: [C]" does NOT have the solution set:  "{0}" ;
 and is not the correct answer; (and is not a correct answer).

The answer is:   [A]:   " -14m − 7m + 1  =  -7m + 1 " .