$\text{a)}$  

$\left|\left|x\right|-3\right|<2$  

$\left|x\right|-3<2\text{i}\left|x\right|-3>-2$  

$\left|x\right|<5\text{i}\left|x\right|>1$  

$x\in \left(-5,5\right)\text{i}x\in \left(-\infty ,-1\right)\cup \left(1,+\infty \right)$  

Zatem:

$x\in \left(-5,-1\right)\cup \left(1,5\right)$  

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$\text{b)}$  

$\left|\left|x\right|+4\right|>5$  

$\left|x\right|+4>5\text{lub}\left|x\right|+4<-5$  

$\left|x\right|>1\text{lub}\left|x\right|<-9$  

$x\in \left(-\infty ,-1\right)\cup \left(1,+\infty \right)\text{lub}\text{sprzecznosˊcˊ}$  

$x\in \left(-\infty ,-1\right)\cup \left(1,+\infty \right)$  

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$\text{c)}$  

$\left|\left|x+4\right|-3\right|>2$  

$\left|x+4\right|-3>2\text{lub}\left|x+4\right|-3<-2$  

$\left|x+4\right|>5\text{lub}\left|x+4\right|<1$  

$\left(x+4>5\text{lub}x+4<-5\right)\text{lub}\left(x+4<1\text{i}x+4>-1\right)$  

$\left(x>1\text{lub}x<-9\right)\text{lub}\left(x<-3\text{i}x>-5\right)$  

$x\in \left(-\infty ,-9\right)\cup \left(1,+\infty \right)\text{lub}x\in \left(-5,-3\right)$  

$x\in \left(-\infty ,-9\right)\cup \left(-5,-3\right)\cup \left(1,+\infty \right)$  

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$\text{d)}$  

$\left|\left|2x-1\right|+2\right|\ge 3$  

$\left|2x-1\right|+2\ge 3\text{lub}\left|2x-1\right|+2\le -3$  

$\left|2x-1\right|\ge 1\text{lub}\left|2x-1\right|\le -5$  

$2x-1\ge 1\text{lub}2x-1\le -1\text{lub}\text{sprzecznosˊcˊ}$  

$2x\ge 2\text{lub}2x\le 0$  

$x\ge 1\text{lub}x\le 0$  

$x\in (-\infty ,0⟩\cup ⟨1,+\infty )$  

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$\text{e)}$  

$\left|\left|2-x\right|+5\right|\le 6$  

$\left|\left|x-2\right|+5\right|\le 6$  

$\left|x-2\right|+5\le 6\text{i}\left|x-2\right|+5\ge -6$  

$\left|x-2\right|\le 1\text{i}\left|x-2\right|\ge -11$  

$x-2\le 1\text{i}x-2\ge -1\text{i}x\in R$  

$x\le 3\text{i}x\ge 1$  

$x\in ⟨1,3⟩$  

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$\text{f)}$  

$\left|7-\right|2x+1\mid \mid \ge 7$  

$\left|\left|2x+1\right|-7\right|\ge 7$  

$\left|2x+1\right|-7\ge 7\text{lub}\left|2x+1\right|-7\le -7$  

$\left|2x+1\right|\ge 14\text{lub}\left|2x+1\right|\le 0$  

$2x+1\ge 14\text{lub}2x+1\le -14\text{lub}2x+1=0$  

$2x\ge 13\text{lub}2x\le -15\text{lub}2x=-1$  

$x\ge \frac{13}{2}\text{lub}x\le -\frac{15}{2}\text{lub}x=-\frac{1}{2}$  

$x\in (-\infty ,-7\frac{1}{2}⟩\cup \left\{-\frac{1}{2}\right\}\cup ⟨6\frac{1}{2},+\infty )$