[tex]\it\ a)\ |x|<2 \Rightarrow -2<x<2\ \Rightarrow x\in(-2,\ \ 2)\\ \\ b)\ |x-2|\leq3 \Rightarrow -3\leq x-2\leq3|_{+2} \Rightarrow -1\leq x\leq5 \Rightarrow x\in[-1,\ \ 5]\\ \\ c)\ \ |1-x|\leq0 \Rightarrow |x-1|\leq0 \Rightarrow x-1=0 \Rightarrow x=1[/tex]
[tex]d)\ -15|x-1|>-105\Big|_{:(-15)} \Rightarrow |x-1|<7 \Rightarrow x-1\in(-7,\ 7)|_{+1} \Rightarrow x\in(-6,\ 8)\\ \\ e)\ 3-|4x-1|\geq0 \Rightarrow |4x-1|\leq3 \Rightarrow 4x-1\in[-3,\ 3]|_{+1} \Rightarrow 4x\in[-2,\ 4]|_{:4} \Rightarrow \\ \\ \Rightarrow x\in\Big[-\dfrac{1}{2},\ \ 1\Big]\\ \\ \\ f)\ |x|\cdot(x-4)>0 \Rightarrow \begin{cases} \it |x|\ne0 \Rightarrow x\ne0\\ \\ x-4>0 \Rightarrow x>4 \Rightarrow x\in(4,\ \infty)\end{cases} \Rightarrow S=(4,\ \ \infty)[/tex]
