Question 888045
Look for the critical values and test in the intervals around each critical value.


You have {{{2x^2+x-3}}}.  Where would this be zero?  That tells you the critical values where the sign of the expression changes.


Factorable?
(2x__  3)(x__  1),   makes 3x and 2x.  We want the 2x to be negative signed.
{{{highlight_green((2x+3)(x-1)=2x^2+x-3)}}}


We have then {{{(2x+3)(x-1)=2x^2+x-3>0}}}.
The critical values for x are at -3/2 and 1.
Pick any one point within each interval and check the sign of the expression.
The intervals are {{{-infinity<x<-3/2}}};
{{{-3/2<x<1}}};
{{{1<x<infinity}}}.


ANY point within each interval!  Let x=-4, or -5, or -10, no matter.  Is the inequality statement true or false?
Let x=-1 or x=0, or whatever in the interval.  Inequality true or false?

Let x= something greater than 1.... What happens?


Inequalities do not have a representation in this web system, but maybe you can handle a graph?  Cartesian graph, since the inequality is based on a parabola?


{{{graph(300,300,-5,5,-10,10,2x^2+x-3)}}}


Obviously the given inequality is true for x less than -3/2  or x greater than 1.