Wiki-Quellcode von Lösung Lösen von linearen Ungleichungen
Verstecke letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
 |
1.1 | 1 | (%class=abc%) |
| |
2.1 | 2 | 1. (((__Rechnerisch:__ |
| |
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 | |||
| |
2.1 | 12 | Lösungsmenge: {{formula}}\text{L}=]-1;\infty[{{/formula}} |
| 13 | |||
| 14 | __Grafisch:__ | ||
| |
7.1 | 15 | |
| 16 | [[image:a).png||width="400"]] | ||
| 17 | |||
| 18 | Man sieht, dass die Gerade mit der Gleichung {{formula}}y=-2x + 3{{/formula}} (grün) für {{formula}}x>-1{{/formula}}unterhalb der Geraden mit der Gleichung {{formula}}y=5{{/formula}} (rot) liegt. | ||
| |
1.1 | 19 | ))) |
| |
2.1 | 20 | 1. (((__Rechnerisch:__ |
| |
1.1 | 21 | |
| 22 | {{formula}} | ||
| 23 | \begin{align*} | ||
| 24 | 3(x + 4) &\geq 6 \\ | ||
| 25 | 3x + 12 &\geq 6 \quad &&\mid -12\\ | ||
| 26 | 3x &\geq -6 \quad &&\mid :3 \\ | ||
| 27 | x &\geq -2 | ||
| 28 | \end{align*} | ||
| 29 | {{/formula}} | ||
| 30 | |||
| |
2.1 | 31 | Lösungsmenge: {{formula}}\text{L}=[-2;\infty[{{/formula}} |
| 32 | |||
| 33 | __Grafisch:__ | ||
| |
7.1 | 34 | |
| 35 | [[image:b).png||width="400"]] | ||
| |
1.1 | 36 | ))) |
| |
2.1 | 37 | 1. (((__Rechnerisch:__ |
| |
1.1 | 38 | |
| 39 | {{formula}} | ||
| 40 | \begin{align*} | ||
| 41 | 5 - 3x &> 4(x - 0.5) \\ | ||
| 42 | 5 - 3x &> 4x - 2 \quad &&\mid -5 \quad -4x\\ | ||
| 43 | -7x &> -7 \quad &&\mid :(-7)\\ | ||
| 44 | x &< 1 | ||
| 45 | \end{align*} | ||
| 46 | {{/formula}} | ||
| 47 | |||
| |
2.1 | 48 | {{formula}}\text{L}=]-\infty;1[{{/formula}} |
| 49 | |||
| 50 | __Grafisch:__ | ||
| |
7.1 | 51 | |
| 52 | [[image:c).png||width="400"]] | ||
| |
1.1 | 53 | ))) |
| |
2.1 | 54 | 1. (((__Rechnerisch__: |
| |
1.1 | 55 | |
| 56 | {{formula}} | ||
| 57 | \begin{align*} | ||
| 58 | 6 + 3(x - 1) &\leq 4(x + 3(x - 1)) - 8x \\ | ||
| 59 | 6 + 3x - 3 &\leq 4(4x - 3) - 8x \\ | ||
| 60 | 3x + 3 &\leq 16x - 12 - 8x \\ | ||
| 61 | 3x + 3 &\leq 8x - 12 \quad &&\mid -8x \quad \mid -3\\ | ||
| 62 | -5x &\leq -15 \quad &&\mid :(-5) \\ | ||
| 63 | x &\geq 3 | ||
| 64 | \end{align*} | ||
| 65 | {{/formula}} | ||
| 66 | |||
| |
2.1 | 67 | {{formula}}\text{L}=[3;\infty[{{/formula}} |
| 68 | |||
| 69 | __Grafisch__: | ||
| |
7.1 | 70 | |
| 71 | [[image:d).png||width="400"]] | ||
| |
1.1 | 72 | ))) |
| 73 |