Bestimmen Sie alle x der folgenden Ungleichungen :
1. \(\frac{x-2}{x+5}>0\) \(\quad\quad\quad ,x_{1}\in\) ❌ \(\cup\) ❌

2. \(\frac{1}{1-x}+\frac{2}{3x-3}>0\) \(\quad\quad\quad ,x_{2}\in\) ❌

3. \(x-|2x-12| \ge 0\) \(\quad\quad\quad ,x_{3}\in\) ❌

4. \(|x+1|-|2x-6| \le 10\) \(\quad\quad\quad ,x_{4}\in\) ❌

5. \(\sqrt{x^2 -5}<8\) \(\quad\quad\quad ,x_{5}\in\) ❌ \(\cup\) ❌

6. \(\sqrt{x+1}<\sqrt{3x-9}\) \(\quad\quad\quad ,x_{6}\in\) ❌

7. \(\log_{2} x + \log_{2} 3 \le \log_{2} 6\) \(\quad\quad\quad ,x_{7}\in\) ❌

8. \(2^{x^2 -x -10} \le \frac{1}{16}\) \(\quad\quad\quad ,x_{8}\in\) ❌

9. \(e^{x} -2e^{-x} \ge 1\) \(\quad\quad\quad ,x_{9}\in\) ❌

10. \(\frac{\sqrt{|x-2|}}{x-1}<1\) \(\quad\quad\quad ,x_{10}\in\) ❌ \(\cup\) ❌

\(]-\infty,-5[\)
\(]-\infty,-5[\)
\(]2,\infty[\)
\(]2,\infty[\)
\(]-\infty,1[\)
\(]-\infty,1[\)
\([4,12]\)
\([4,12]\)
\(\mathbb{R}\)
\(\mathbb{R}\)
\(]-\sqrt{69},-\sqrt{5}]\)
\(]-\sqrt{69},-\sqrt{5}]\)
\([\sqrt{5},\sqrt{69}[\)
\([\sqrt{5},\sqrt{69}[\)
\(]5,\infty[\)
\(]5,\infty[\)
\(]0,2]\)
\(]0,2]\)
\([-2,3]\)
\([-2,3]\)
\(keine\ Lösung = x\notin\mathbb{R}\)
\(keine\ Lösung = x\notin\mathbb{R}\)
\(]-\infty,1[_{für\ 10.}\)
\(]-\infty,1[_{für\ 10.}\)
\(]\frac{1+\sqrt{5}}{2},\infty[\)
\(]\frac{1+\sqrt{5}}{2},\infty[\)