Question 349089
{{{6x-5>=6/x}}}
Plot {{{y=6x-5}}}
{{{drawing(300,300, -5,5,-12,8,grid(1),graph(300,300, -5,5,-12,8,6x-5))}}}
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In addition now plot {{{y=6/x}}}
{{{drawing(300,300, -5,5,-12,8,grid(1),graph(300,300, -5,5,-12,8,6x-5,6/x))}}}
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Find the intersection points, where {{{6x-5=6/x}}}
{{{6x^2-5x=6}}}
{{{6x^2-5x-6=0}}}
{{{(3x+2)(2x-3)=0}}}
Two solutions:
{{{3x+2=0}}}
{{{3x=-2}}}
{{{x=-2/3}}}
Then 
{{{y=6(-2/3)-5}}}
{{{y=-4-5}}}
{{{y=-9}}}
(-2/3,-9)
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{{{2x-3=0}}}
{{{2x=3}}}
{{{x=3/2}}}
Then
{{{y=6/(3/2)}}}
{{{y=4}}}
(3/2,4)
Plot those points.
{{{drawing(300,300, -5,5,-12,8,blue(line(-2/3,10,-2/3,-20)),blue(line(3/2,10,3/2,-20)),circle(3/2,4,0.3),circle(-2/3,-9,0.3),grid(1),graph(300,300,-5,5,-12,8,6x-5,6/x))}}}
Now look for the regions where the red line is above the green curve.
Solution region:({{{-2/3}}},{{{0}}})U({{{3/2}}},{{{infinity}}})