Question 869249
First find the points where the functions cross each other.
{{{f(x)=g(x)}}}
{{{x^2-4x=x-6}}}
{{{x^2-5x+6=0}}}
{{{(x-2)(x-3)=0}}}
Two solutions:
{{{x-2=0}}}
{{{x=2}}}
and
{{{x-3=0}}}
{{{x=3}}}
So break up the number line into three regions and test the inequality.
{{{x<2}}}
{{{x=0}}}
{{{0-4>0-6}}}
{{{-4>-6}}}
True
{{{2<x<3}}}
{{{x=5/2}}}
{{{(5/2)^2-4(5/2)>5/2-6}}}
{{{25/4-20/2>5/2-12/2}}}
{{{25/4-40/4>-7/2}}}
{{{-15/4>-14/4}}}
False
{{{x>3}}}
{{{x=4}}}
{{{4^2-4(4)>4-6}}}
{{{0>-2}}}
True
So now put it all together.
({{{-infinity}}},{{{2}}}]U[{{{3}}},{{{infinity}}})