Question 1200141
The second inequality

{{{k(2k-3)<k^2-2}}}
{{{2k^2-3k<k^2-2}}}
{{{k^2-3k+2<0}}}
{{{(k-2)(k-1)<0}}}


Important values to check around on number line are +1 and +2.

To left of k=1
(0-2)(0-1)
(-2)(-1)<0 FALSE

Between the two values
(1.5-2)(1.5-1)
(-)(+)<0 TRUE

To Right of k=2
(3-2)(3-1)
(+)(+)<0 FALSE


SOLUTION:  {{{highlight(1<k<2)}}}