Question 124822
{{{5+X<2X+1<6-X}}}


There are actually two relationships established here.  Deal with each one separately.

{{{5+x<2x+1}}}


Add -1 to each side.
{{{4+x<2x}}}


Add -x to each side.
{{{4<x}}}


Now look at the other relationship
{{{2x+1<6-x}}}


Add -1 to each side
{{{2x<5-x}}}


Add x to each side
{{{3x<5}}}


Divide by 3.  (since we are dividing by a positive number, we keep the sense of the inequality as it is)
{{{x<5/3}}}


So, x must simultaneously be less than 5/3 and greater than 4.  Impossible.  There is no value of x that makes the original inequality a true statement.