Question 846031
Subtract 7 from both sides.
{{{(x+16)/(x-2)-7((x-2)/(x-2))<=0}}}
{{{(x+16-7x+14)/(x-2)<=0}}}
{{{(-6x+30)/(x-2)<=0}}}
Look at the zeros of the numerator and the undefined values of the denominator and break up the number line. 
{{{x=5}}}
{{{x=2}}}
Test for values less than 2, between 2 and 5, and greater than 5.
First, less than 2, {{{x=0}}},{{{30/(-2)<=0}}}, {{{-15<=0}}}, True.
Between 2 and 5, {{{x=3}}}, {{{(-18+30)/(3-2)<=0}}},{{{12<=0}}}, False.
Greater than or equal to 5, {{{x=6}}}, {{{(-6(6)+30)/(6-2)<=0}}},{{{-6/3<=0}}},{{{-2<=0}}}, True.
So the solution set is,
({{{-infinity}}},{{{2}}})U[{{{5}}},{{{infinity}}})