Question 805756
(1/2)|2w-1|-3>1
{{{(1/2)*abs(2w-1)-3>1}}}


Handle the absolute value function as a variable.  Solve for it:


{{{abs(2w-1)>2(1+3)}}}
{{{abs(2w-1)>8}}}


Solve based on each of the two conditions:


The argument is positive or zero, {{{2w-1>=0}}}.
{{{2w-1>8}}}
{{{2w>8+1}}}
{{{2w>9}}}
{{{w>9/2}}}


The argument may be negative, {{{2w-1<0}}}.
{{{abs(2w-1)=-(2w-1)=1-2w}}}.
{{{1-2w>8}}}
{{{-2w>8+1}}}
{{{-2w>9}}}
Next step requires care;
{{{-2w(-1/2)<9*(-1/2)}}}
{{{w<-9/2}}}


Combine the two results to complete the answer.
{{{highlight(w<-9/2)}}} OR {{{highlight(w>9/2)}}}.