Question 1192806
<pre>

{{{abs(x)+abs(2-x)}}}{{{""<""}}}{{{2}}}

Use the definition of absolute value {{{abs(N)=sqrt(N^2)}}}

{{{sqrt(x^2)+sqrt((2-x)^2)}}}{{{""<""}}}{{{2}}}

Isolate the more complicated square root on the left:

{{{sqrt((2-x)^2)}}}{{{""<""}}}{{{2-sqrt(x^2)}}}

Square both sides:

{{{(sqrt((2-x)^2))^2}}}{{{""<""}}}{{{(2-sqrt(x^2))^2}}}

{{{(2-x)^2}}}{{{""<""}}}{{{(2-sqrt(x^2))^2}}}

{{{4-4x+x^2}}}{{{""<""}}}{{{4-4sqrt(x^2)+x^2}}}

{{{-4x}}}{{{""<""}}}{{{-4sqrt(x^2)}}}

Divide both sides by -4 which flips the < to >:

{{{x}}}{{{"">""}}}{{{sqrt(x^2)}}}

This can never be true because if x were positive,
equality would hold.   If x were 0, equality would
hold, and if x were negative, < would hold.

So the inequality is a contradiction.

Edwin</pre>