1-7n=8+2n

First, get all the variable terms to one side; remove the smaller variable;

remove -7n by adding 7n to both sides:

1 - 7n  =  8 + 2n

1 - 7n + 7n  =  8 + 2n + 7n

1  =  8 + 9n

Remove the 8 by subtracting 8 from both sides:

1 - 8  =  8 - 8 + 9n

-7  =  9n

Divide both sides by 9:
-7/9  =  n