Wiki-Quellcode von Lösung Lösen von linearen Ungleichungen
Verstecke letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
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1.1 | 1 | (%class=abc%) |
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2.1 | 2 | 1. (((__Rechnerisch:__ |
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1.1 | 3 | |
| 4 | {{formula}} | ||
| 5 | \begin{align*} | ||
| 6 | -2x + 3 &< 5 \quad &&\mid -3\\ | ||
| 7 | -2x &< 2 \quad &&\mid :(-2)\\ | ||
| 8 | x &> -1 | ||
| 9 | \end{align*} | ||
| 10 | {{/formula}} | ||
| 11 | |||
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2.1 | 12 | Lösungsmenge: {{formula}}\text{L}=]-1;\infty[{{/formula}} |
| 13 | |||
| 14 | __Grafisch:__ | ||
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1.1 | 15 | ))) |
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2.1 | 16 | 1. (((__Rechnerisch:__ |
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1.1 | 17 | |
| 18 | {{formula}} | ||
| 19 | \begin{align*} | ||
| 20 | 3(x + 4) &\geq 6 \\ | ||
| 21 | 3x + 12 &\geq 6 \quad &&\mid -12\\ | ||
| 22 | 3x &\geq -6 \quad &&\mid :3 \\ | ||
| 23 | x &\geq -2 | ||
| 24 | \end{align*} | ||
| 25 | {{/formula}} | ||
| 26 | |||
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2.1 | 27 | Lösungsmenge: {{formula}}\text{L}=[-2;\infty[{{/formula}} |
| 28 | |||
| 29 | __Grafisch:__ | ||
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1.1 | 30 | ))) |
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2.1 | 31 | 1. (((__Rechnerisch:__ |
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1.1 | 32 | |
| 33 | {{formula}} | ||
| 34 | \begin{align*} | ||
| 35 | 5 - 3x &> 4(x - 0.5) \\ | ||
| 36 | 5 - 3x &> 4x - 2 \quad &&\mid -5 \quad -4x\\ | ||
| 37 | -7x &> -7 \quad &&\mid :(-7)\\ | ||
| 38 | x &< 1 | ||
| 39 | \end{align*} | ||
| 40 | {{/formula}} | ||
| 41 | |||
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2.1 | 42 | {{formula}}\text{L}=]-\infty;1[{{/formula}} |
| 43 | |||
| 44 | __Grafisch:__ | ||
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1.1 | 45 | ))) |
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2.1 | 46 | 1. (((__Rechnerisch__: |
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1.1 | 47 | |
| 48 | {{formula}} | ||
| 49 | \begin{align*} | ||
| 50 | 6 + 3(x - 1) &\leq 4(x + 3(x - 1)) - 8x \\ | ||
| 51 | 6 + 3x - 3 &\leq 4(4x - 3) - 8x \\ | ||
| 52 | 3x + 3 &\leq 16x - 12 - 8x \\ | ||
| 53 | 3x + 3 &\leq 8x - 12 \quad &&\mid -8x \quad \mid -3\\ | ||
| 54 | -5x &\leq -15 \quad &&\mid :(-5) \\ | ||
| 55 | x &\geq 3 | ||
| 56 | \end{align*} | ||
| 57 | {{/formula}} | ||
| 58 | |||
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2.1 | 59 | {{formula}}\text{L}=[3;\infty[{{/formula}} |
| 60 | |||
| 61 | __Grafisch__: | ||
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1.1 | 62 | ))) |
| 63 |