$\displaystyle \frac{2}{x-1} > 3$

Now I know the answer is 1 < X < 5/3 but I'm trying to work through it.

I can work it out for 5/3 but I'm not sure how I'm meant to solve for 1.

$\displaystyle 2 > 3x - 3$

$\displaystyle 5 > 3x$

$\displaystyle \frac{5}{3} > x$

Just got a mind blank as to how I'm meant to solve it to get 1 as the other case.