Zadanie 1
[tex]\sqrt{5}(|x+1|-2|-x-1|)>-2\\\\\sqrt{5}(|x+1|-2|-(x+1)|)>-2\\\\\sqrt{5}(|x+1|-2|x+1|)>-2\\\\\sqrt{5}(-|x+1|)>-2\\\\-\sqrt{5}|x+1|>-2\\\\\sqrt{5}|x+1|<2\\\\|x+1|<\dfrac{2}{\sqrt{5}}\\\\|x+1|<\dfrac{2\sqrt{5}}{5}[/tex]
[tex]x+1<\dfrac{2\sqrt{5}}{5}\quad\text{i}\quad x+1>-\dfrac{2\sqrt{5}}{5}\\\\x<\dfrac{2\sqrt{5}-5}{5}\quad\text{i}\quad x>\dfrac{-2\sqrt{5}-5}{5}\\\\\boxed{x\in\Big(\dfrac{-5-2\sqrt{5}}{5},\dfrac{-5+2\sqrt{5}}{5}\Big)}[/tex]
Zadanie 2
[tex]15+2\sqrt{5}|x+3|\leq 2\sqrt{20}|-3-x|\\\\15+2\sqrt{5}|x+3|\leq 2\sqrt{4\cdot 5}\cdot|-(x+3)|\\\\15+2\sqrt{5}|x+3|\leq 4\sqrt{5}|x+3|\\\\2\sqrt{5}|x+3|\geq 15\\\\|x+3|\geq\dfrac{15}{2\sqrt{5}}\\\\|x+3|\geq\dfrac{15\sqrt{5}}{10}[/tex]
[tex]x+3 \geq\dfrac{15\sqrt{5}}{10}\quad\text{lub}\quad x+3\leq-\dfrac{15\sqrt{5}}{10}\\\\x\geq\dfrac{15\sqrt{5}-30}{10}\quad\text{lub}\quad x\leq\dfrac{-15\sqrt{5}-30}{10}\\\\\boxed{x\in\Big(-\infty,\dfrac{-30-15\sqrt{5}}{10}\Big\rangle\cup\Big\langle\dfrac{-30+15\sqrt{5}}{10},+\infty\Big)}[/tex]
