karthikpandian19 wrote:What is the value of |x−2|?
(1) |x−4|=2
(2) |2−x|=4
$$? = \left| {x - 2} \right|$$
$$\left( 1 \right)\,\,\,{\rm{dist}}\left( {x,4} \right) = \left| {x - 4} \right| = 2\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{
\,x = 6\,\,\,\, \Rightarrow \,\,\,\,? = 4 \hfill \cr
\,x = 2\,\,\,\, \Rightarrow \,\,\,\,? = 0 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.$$
$$\left( 2 \right)\,\,\,4 = \,\,\left| {2 - x} \right|\,\,{\rm{ = }}\,\,\left| {x - 2} \right|\,\,\,{\rm{ = }}\,\,\,{\rm{?}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
