1:   < 


    Multiply both sides of the inequality by 120 to get


    10*(x+8) < 12*(x-1)

    10x + 80 < 12x - 12

    80 + 12 < 12x - 10x

    92 < 2x


     Divide both sides by 2 to get the  ANSWER :  x > 46.




3.  x^2 - x + 1 > 1


    It is equivalent to


    x^2 - x > 0

    x*(x-1) > 0


    Case a):  both factors are positive :  x > 0 and x-1 > 0.

              The set of solutions is  { x > 1}.



    Case b):  both factors are negative :  x < 0  and x-1 < 0.

              The solution set is  x < 0.


ANSWER.  The solution set for the given inequality is the union of two semi-infinite intervals  (,) U (,).

        One and only one problem / question per post