Step 1:          7 + 3x + 2 = –2x + 4
Step 2:             10x + 2 = –2x + 4

In going from step 1 to step 2, the error was adding unlike terms
7 and 3x.  Step 2 should have been to combine the like terms 7 and 2
and get 9 + 3x = -2x + 4


Step 2:             10x + 2 = –2x + 4
Step 3:              8x + 2 = 4

In going from step 2 to step 3, the error was adding 2x to the right side
yet adding -2x to the left side terms.  If step 2 had been correct, Step 3
would have been to add 2x to the left side and get 12x + 2 = 4


Step 3:              8x + 2 = 4
Step 4:                  8x = 2

Going from step 3 to step 4 was correct, since -2 was added to both sides. 

Step 4:                  8x = 2
Step 5:                   x = 4

In going from step 4 to step 5, the error was in dividing 8 by 2 instead of
dividing 2 by 8.  If step 4 had been correct, Step 5 would have x = 
and then reduce  the fraction to x = .

Edwin