Question

|3x+5|>20 2)|7-4x|<11 3)|4+3x|<5

Answer 1

$1)\; \; |3x+5|>20\; \; \to \; \; \; \left [ {{3x+5>20} \atop {3x+5<-20}} \right. \; \; \left [ {{3x>15} \atop {3x<-25}} \right.\; \; \left [ {{x>5} \atop {x<-8\frac{1}{3}}} \right.\\\\x\in (-\infty ,-8\frac{1}{3})\cup (5,+\infty )$

$2)\; \; |7-4x|<11\; \; \to \; \; \; -11<7-4x<11\; ,\\\\-18<-4x<4\; \; \; ,\; \; \; -4<4x<18\; \; ,\; \; -1<x<4,5\\\\x\in (-1\, ;\; 4,5)$

$3)\; \; |4+3x|<5\; \; \to \; \; \; -5<4+3x<5\; ,\\\\-9<3x<1\; \; ,\; \; \; -3<x<\frac{1}{3}\\\\x\in (-3,\frac{1}{3}\; )$