Question 1093977
{{{(x+9)/x>=6}}}
{{{(x+9)/x-6>=0}}}
{{{(x+9-6x)/x>=0}}}
{{{(9-5x)/x>=0}}}
The numerator and denominator change signs (from positive to negative)
at {{{x=9/5=1.8}}} and {{{x=0}}} respectively .
For {{{0<x<=9/5}}} , {{{system(x>0,9-5x>=0)}}} and {{{(9-5x)/x>=0}}} ,
For {{{x=0}}} , {{{(x+9)/x>=6}}} is undefined,
For all other real values of {{{x}}} , meaning {{{system(x<0,"or",x>9/5)}}} ,
{{{(9-5x)/x<0}}} .
So, {{{highlight0<x<=9/5)}}} is the solution.