Just to put in my oar: 8x- 3 says "first multiply x by 8 and then subtract 3".
The "inverse" is the inverse of the original operarations ("divide by 8" rather than "multiply by 8" and "add 3" rather than "subtract 3") done in the opposite order.
So the inverse of "first multiply x by 8 and then subtract 3" is "first add 3 to x and then divide by 8".