31975550
Description
Quiz by IWKZ Tutorium, updated more than 1 year ago
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Created by IWKZ Tutorium
almost 3 years ago
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Question 1
Question
Bestimmen Sie alle x der folgenden Ungleichungen :
1. \(\frac{x-2}{x+5}>0\) \(\quad\quad\quad ,x_{1}\in\) [blank_start]a[blank_end] \(\cup\) [blank_start]b[blank_end]
2. \(\frac{1}{1-x}+\frac{2}{3x-3}>0\) \(\quad\quad\quad ,x_{2}\in\) [blank_start]a[blank_end]
3. \(x-|2x-12| \ge 0\) \(\quad\quad\quad ,x_{3}\in\) [blank_start]a[blank_end]
4. \(|x+1|-|2x-6| \le 10\) \(\quad\quad\quad ,x_{4}\in\) [blank_start]a[blank_end]
5. \(\sqrt{x^2 -5}<8\) \(\quad\quad\quad ,x_{5}\in\) [blank_start]a[blank_end] \(\cup\) [blank_start]b[blank_end]
6. \(\sqrt{x+1}<\sqrt{3x-9}\) \(\quad\quad\quad ,x_{6}\in\) [blank_start]a[blank_end]
7. \(\log_{2} x + \log_{2} 3 \le \log_{2} 6\) \(\quad\quad\quad ,x_{7}\in\) [blank_start]a[blank_end]
8. \(2^{x^2 -x -10} \le \frac{1}{16}\) \(\quad\quad\quad ,x_{8}\in\) [blank_start]a[blank_end]
9. \(e^{x} -2e^{-x} \ge 1\) \(\quad\quad\quad ,x_{9}\in\) [blank_start]a[blank_end]
10. \(\frac{\sqrt{|x-2|}}{x-1}<1\) \(\quad\quad\quad ,x_{10}\in\) [blank_start]a[blank_end] \(\cup\) [blank_start]b[blank_end]
Answer
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\(]-\infty,-5[\)
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\(]2,\infty[\)
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\(]-\infty,1[\)
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\([4,12]\)
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\(\mathbb{R}\)
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\(]-\sqrt{69},-\sqrt{5}]\)
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\([\sqrt{5},\sqrt{69}[\)
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\(]5,\infty[\)
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\(]0,2]\)
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\([-2,3]\)
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\(keine\ Lösung = x\notin\mathbb{R}\)
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\(]-\infty,1[_{für\ 10.}\)
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\(]\frac{1+\sqrt{5}}{2},\infty[\)
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