Linear Equation with Only One Solution?

I need help to understand this problem. It says to find exactly one solution but doesn't the second answer and the third answer provide only one solution just like the first one?

I might be wrong, but the second answer left me with [ x = -62 ], and the third answer left me with [ x = -29 ].

For the second answer, I set up my problem like 2x + 31 = 2x - 31. Then I subtracted 31 from the left side and subtracted it from the right, which leaves 2x = 2x - 62? Finally, I subtracted the 2x from the right side and then from the left side to single out the x and constant, which left me with [ x = -62 ].

Clearly, I got the second and third answer wrong except for the first, so what am I doing wrong?