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|x| > a

=>x > a or x < -a(if a [itex]\in[/itex] R

^{+}and x [itex]\in[/itex] R if a [itex]\in[/itex] R

^{-}

|x|<a

=> -a < x < a if a [itex]\in[/itex] R

^{+}and no solution if a [itex]\in[/itex] R

^{-}[itex]\cup[/itex]{0}

If yes, then examples please?(for instances in x and a)

Blindly apply these equations we can solve |x-1| >= 3 as x-1<= -3 or x-1 >=3

If yes then how can we solve a inequality like |x-1| - |x| + |2x+3| > 2x +4 using the same logical statements above?