Question 972800
{{{abs(7x-9)>=abs(x+3)}}}


To be easy, either the signs of each argument are same or they are opposite.  Examining the simple cases would be better for understanding, but avoiding here.


You want both of these to be true for a solution.
{{{7x-9>=x+3}}}  AND  {{{7x-9>=-x-3}}}


-
-
{{{6x-12>=0}}}
{{{x-2>=0}}}
{{{x>=2}}}


{{{8x-6>=0}}}
{{{8x>=6}}}
{{{4x>=3}}}
{{{x>=3/4}}}


The first condition makes {{{x>=2}}}; and the second condition makes {{{x>=3/4}}}.  We can check intervals around the critical x values just to be more certain.


Between the two:
{{{abs(7x-9)>=abs(x+3)}}}
pick 1.
{{{abs(7*1-9)>=abs(1+3)}}}
{{{abs(-2)>=abs(4)}}}
{{{2>=4}}}, FALSE.


Left of 3/4:
pick 0.
{{{abs(7*0-9)>=abs(0+3)}}}
{{{abs(-9)>=abs(3)}}}
{{{9>=3}}}, TRUE.


Greater than 2:
pick 3.
{{{abs(7*3-9)>=abs(3+3)}}}
{{{12>=6}}}, TRUE.


Actual answer is {{{highlight(x>=3/4)}}}.