Question 13510
{{{3-abs(2x+4)>=1}}}

{{{abs(2x+4)}}} =
(i) 2x + 4; where {{{2x+4>=0}}} or {{{x>=-2}}}
(ii) -(2x+4); where {{{2x+4<0}}} or {{{x<-2}}}

Case (i):

{{{3-(2x+4)>=1}}}; where {{{x>=-2}}}
{{{3-2x-4>=1}}}
{{{-2x>=1+4-3}}}
{{{-2x>=2}}}
{{{(-2x)/(-2)<=2/(-2)}}}
{{{x<=-1}}}
Solution for this case is {{{-2<=x<=-1}}}

Case (ii):

{{{3-(-(2x+4))>=1}}}; where {{{x<-2}}}
{{{3+(2x+4)>=1}}}
{{{3+2x+4>=1}}}
{{{2x+4+3>=1}}}
{{{2x+7>=1}}}
{{{2x>=1-7}}}
{{{2x>=-6}}}
{{{2x/2>=-6/2}}}
{{{x>=-3}}}
Solution for this case is {{{-3<=x<-2}}}

Combine case (i) and (ii), so:{{{-3<=x<=-1}}}

OK