1)
$ \dfrac{2}{x-1} > 1$
$\to 2 > x-1$
$ \to x - 1 -2 < 0 $
$\to x -3 < 0$
$\to x > 3$
2)
$ -3x < -7x+5$
$\to -3x + 7x -5 < 0$
$\to 4x -5 < 0$
$\to 4x < 5$
$\to x < \dfrac{5}{4}$
3)
$ 4 - 7x \le 4x -2$
$\to 4 -7x - 4x +2 \le 0$
$\to - 11x + 6 \le 0$
$\to -11x \le -6$
$\to x \ge \dfrac{6}{11}$
4)
$ -4x +3 \le 5x -7$
$\to -4x +3 -5x +7 \le 0$
$\to -9x +10 \le 0$
$\to -9x \le -10$
$\to x \ge \dfrac{10}{9}$