|(x+1)/(4-x)|<=1/2<br>-1/2<=(x+1)/(4-x)<=1/2<br>
(x+1)/(4-x)>=-1/2
(x+1)(4-x)<=1/2<br>
(x+1)/(4-x)+1/2>=0
(x+1)/(4-x)-1/2<=0<br>
(2x+2+4-x)/2(4-x)>=0
(2x+2-4+x)/2(4-x)<=0<br>
(x+6)/2(4-x)>=0
(3x-2)/2(4-x)<=0<br>
(x+6)/(x-4)<=0<br>(3x-2)/(x-4)>=0
равносильно
(x+6)(x-4)<=0 [6,4)<br>(3x-2)(x-4)>=0 (-бескон.,2/3]U(4,+бескон.)
ответ:[-6,2/3]
методом интервалов