Question 930503
Analyze the equation logically.  The absolute value inputs can be greater-than-or-equal to zero, or less than zero.



If both nonzero, then {{{x+1+1-x=2}}}
{{{2=2}}}; and you can find what must be x for both inputs to be nonzero.
{{{x+1>=0}}}
{{{x>=-1}}}
&
{{{1-x>=0}}}
{{{1>=x}}}
{{{x<=1}}}
Meaning:
{{{highlight(-1<=x<=1)}}}



IF both are negative, then {{{-x-1+(-1)+x=2}}}
{{{-2=2}}} FALSE statement.  Obviously both expressions in the absolute value inputs must not be simultaneously negative.


If x+1>=0 and 1-x<0, then {{{x+1+(-1)+x=2}}}
{{{2x=2}}}
{{{x=1}}}, which is only a piece of the solution found in {{{-1<=x<=1}}}.


If x+1<0 and 1-x>=0, then {{{-x-1+1-x=2}}}
{{{-2x=2}}}
{{{x=-1}}}, again this one is consistent with the first found inequality solution but is only one piece of it.


FINAL FINISHED ANSWER RESULT:   {{{highlight(-1<=x<=1)}}}