What is x if 8x+4=x-3?

It's -1.
Add three to both sides. 8x+7=x
Subtract the x. 7x+7=0
Subtract 7. 7x=-7
Divide both sides by 7. x=-1
easy

8x + 4 = x - 3 ;; subtract 4 from both sides

8x + 4 - 4 = x - 3 - 4 ;; tidy up

8x = x - 7 ;; subtract x from both sides

8x - x = x - x - 7 ;; tidy up

7x = -7 ;; divide by 7

(7/7)x = -7/7

1x = -1

x = -1.

Check:
8 ⋅ -1 + 4 = -1 - 3

-8 + 4 = - 4

-4 = -4.