When solving for a variable, you undo all operations done to that variable.
In the equation 6x - 3 = -51 we see on the left-hand side that the variable x is being multiplied by 6 and subtracted 3 times.
We can reverse the subtraction operation by using the inverse of subtraction.
Which is the addition operation. If we add 3 to the left-hand side, the -3 term will disappear.
But wait! Anything we do on one side we must do also on the opposite side.
6x - 3 + 3 = -51 + 3
6x = -48
Now how can we undo the multiplication operation done to x?
We can use division. It will make the 6 coefficient disappear!
6x / 6 = -48/6
x = -8
So, x is equal to -8.