-4x + 9 = 2x - 12x + 51
combine like terms...correct
-4x + 9 = -10x + 51
additive inverse ...correct...I think...it could be addition property
6x + 9 = 51
error here....subtraction property was used....subtract 9 from both sides
6x = 42
division property of equality....divide both sides by 6
x = 42/6
simplify
x = 7
summary :
I am not 100% sure on step 3....I would have put addition property
error in step 5....subtraction property was used
error in step 7....6x / 6 = 42/6.....division property was used
error in step 8.....simplifies to x = 7