solve the inequality of x^2-2x-1>3x-7?

Question

could someone please solve the inequality
x^2- 2x -1 >3x- 7
and the inequality of
2x-1/ x-3 < 1
please and thank you

Answer 1

x^2- 2x -1 >3x- 7 is equivalent to
x^2 - 5x + 6 = (x-2)(x-3) > 0
x < 2 or x > 3

(2x-1)/(x-3) < 1 is equivalent to
(2x-1)(x-3) - (x-3)^2 < 0, multiplied each term by (x-3)^2
(x-3)(2x-1-x+3) = (x-3)(x+2) < 0
-2 < x < 3

Answer 2

x^2- 2x -1 >3x- 7
x^2-5x+6 >0
(x-2)(x-3)>0
x <2 and x>3

2x-1/ x-3 < 1
2x-1 < x-3
x < -2