# ` `Dear sir pls ans this inequality question not by squaring both sides as it doesn't work out always.|x^2-2x|+|x-4|>|x^2-3x+4|Thanks

Arun Kumar IIT Delhi
```Hi Jai,$See \\|x^2-2x|+|x-4|>|x^2-3x+4| \\=>|x^2-2x|+|4-x|>|x^2-3x+4|$if you sum the things between modes they are equal.So by trianglethey all should be positive or all negative but that we don't have to do.So on of them should be negative.$A=x^2-2x \\=>B=4-x \\=>C=x^2-3x+4 \\1-A>0,B>0,C<0 \\2-A>0,B<0,C>0 \\3-A<0,B>0,C>0 \\4-A<0,B<0,C>0 \\5-A<0,B>0,C<0 \\6-A>0,B<0,C<0$6 case only few of them will generate common interval for x.Thanks & Regards