how do you solve and graph 7x-7>x-1

Answer 1

7x-7>x-1
As long as you add or subtract terms from each side, the method is
the same as if you had an equation ...
add 7 to both sides
7x > x-1 + 7
7x > x + 6
subtract x from both sides
7x - x > 6
6x > 6

The next step is crucial. If you multiply or divide both sides by a negative
the inequality sign must be reversed
since we are going to divide both sides by 6, it stays the same

x > 1

Usually that last procedure does not happen till the very end, like here