Question 1031982
Identify critical x values and form the intervals on the number line.  Test any value in each interval for truth or false.


{{{x<-3/2}}}
Pick -6.
{{{abs(3(-6)+1)<2+abs(2(-6)+3)}}}
{{{17<2+9}}}
{{{17<11}}}
FALSE


{{{-3/2<x<-1/3}}}
Pick -1.
{{{abs(-3+1)<2+abs(-2+3)}}}
{{{2<2+1}}}
{{{2<3}}}
TRUE


{{{-1/3<x}}}
Pick 0.
{{{1<2+3}}}
TRUE


Just to be clear, ALSO try to check AT each critical value.
{{{0<2+abs(2(-3/2)+3)}}}
{{{0<2}}} TRUE but note that x at  -3/2  is true because you are working with a strict inequality.


Solution is  {{{highlight(x>-3/2)}}}.