Question 1022158
Trying to isolate x may be unworkable.  Split into two inequalities and solve each.


{{{3-x<=x-4}}}
{{{3-x-x<=x-4-x}}}
{{{3-2x<=-4}}}
{{{-2x<=-4-3}}}
{{{-2x<=-7}}}
{{{x>=7/2}}}


AND


{{{x-4<=2x-9}}}
{{{-4<=x-9}}}
{{{-4+9<=x}}}
{{{5<=x}}}


These two separately say  {{{7/2<=x}}} and {{{5<=x}}}.  You might want to check in the intervals
which these critical x values create to see which do and do not satisfy the ORIGINAL combined
inequality.


{{{x<=7/2}}}?  Pick x at 3 to check.
{{{3-x<=x-4<=2x-9}}}
{{{3-(3)<=3-4<=2(3)-9}}}
{{{0<=-1<=-3}}}
Certainly FALSE, as would be expected.


{{{7/2<=x<5}}}?  Pick 4.
{{{3-4<=4-4<=2*4-9}}}
{{{-1<=0<=-1}}}-----<s>TRUE</s>.   Actually FALSE.  


Last interval,  {{{x>=5}}}?
Pick 5.
{{{3-5<=5-4<=2*5-9}}}
{{{-2<=1<=1}}}
TRUE ---- This interval works.


The solution for the combined inequality is  {{{highlight(highlight_green(cross(x>=7/2)))}}}.
No.  Not correct.
Initial solution post had mistake in the work on the middle interval.
The correct solution is  {{{highlight(5<=x)}}}.