#abs(x-2) < abs(2 x+1)# squaring both sides ,
#(x-2)^2 < (2 x+1)^2# or
#x^2-4 x+4 < 4 x^2 +4 x +1# or
#4 x^2 +4 x +1> x^2-4 x+4 # , transposing,
#4 x^2 +4 x +1 - x^2+4 x-4 >0 # or
#3 x^2 +8 x -3 >0 # or
#3 x^2 +9 x - x-3 >0 # or
#3 x( x+3)-1(x+3) >0 # or
#( x+3)(3 x-1) >0 #, critical points are # x=-3, x=1/3
# f(x)=( x+3)(3 x-1) #
Sign chart: When #x <-3 # sign of #f(x)# is #(-)*(-)=(+) :. >0#
When #-3 < x <1/3 # sign of #f(x)# is #(+)*(-)=(-) :. <0#
When #x > 1/3 # sign of #f(x)# is #(+)*(+)=(+) :. >0#
Solution:# x < 3 and x > 1/3 or (-oo, 3)uu(1/3,oo)# [Ans]