Question 1186194
Expression on the left changes sign around 2.
Expression on the right changes sign around 4.


The intervals on the number line are to be checked.
{{{system(x<=2,2<=x<=4,4<=x)}}}.



(1)
{{{-3x+6>=4-x}}}
{{{6-4>=-x+3x}}}
{{{2>=2x}}}
{{{x<=1}}}


(2)
{{{3x-6>=4-x}}}
{{{4x>=10}}}
{{{x>=5/2}}}


(3)
{{{3x-6>=-4+x}}}
{{{4x>=-10}}}
{{{x>=-5/2}}}


Each of those need to be checked to see if they work in the original inequality.


The work above contains a mistake.
The real solution is for {{{x<=1}}} OR {{{x>=2.5}}}.