Cách giải:
$a) (-x + 31) - 39 = -69 + 11$
$→-x+31=-58$
$→-x=-58-31$
$→-x=-89$
$→x=89(TM \,\, x \in Z)$
Vậy x=89
$b) -129 - (35 - x) = 55$
$→35-x=-129-55$
$→35-x=-184$
$→x=35+184=219(TM \,\, x \in Z)$
Vậy x=219
$c) (-37) - |7- x| = -127$
$→|7-x|=-37+127$
$→|7-x|=90$
$→\left[ \begin{array}{l}7-x=90\\x-7=90\end{array} \right.$
$→\left[ \begin{array}{l}x=-83(TM)\\x=97(TM)\end{array} \right.$
$d) |x-14| + (-6) < -4$
$→|x-13|<-4+6=2$
$→-2<x-13<2$
$→11<x<15$
$→x \in {12,13,14}(Do \,\, x \in Z)$
Vậy $x \in {12,13,14}$
$e) 43 + (9 - 21) = 315 - (x + 315)$
$→43-12=315-x-315$
$→31=-x$
$→x=-31(TM \,\, x \in Z)$
Vậy $x=-31$
$f) -7 + |x - 4| = -3$
$→|x-4|=-3+7=4$
$→\left[ \begin{array}{l}x-4=4\\x-4=-4\end{array} \right.$
$→\left[ \begin{array}{l}x=8\\x=0\end{array} \right.$
