Are the equations m+3=-5 and m-4=-12 equivalent

Yes they are because m=-8 in both equations

No, m+3=5 can be simplified to m=5-3 when subtracting 3 on both sides. Then 5-3=2. So the first equation m=2. For the second equation add 4 to both sides to get m=-12+(-4) Then subtract -12+(-4) to get -16.