Algebra: Terme und Gleichungen: Unterschied zwischen den Versionen
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− | * 3x + 10 = 19 | + | * 3x + 10 = 19 | <u style="color:lightgrey;background:lightgrey">- 10 </u> |
<div align="right"><math>\mathbb{G}=\mathbb{Q}</math></div> | <div align="right"><math>\mathbb{G}=\mathbb{Q}</math></div> | ||
Zeile 24: | Zeile 24: | ||
{{Lösung versteckt|1= | {{Lösung versteckt|1= | ||
− | ::<math> \ 3x + 10 = 19 | + | ::<math> \ 3x + 10 = 19 | - 10 </math> |
− | ::<math>\Leftrightarrow 3x = 9 | + | ::<math>\Leftrightarrow 3x = 9 | : 3 </math> |
::<math>\Leftrightarrow x = 3 </math> | ::<math>\Leftrightarrow x = 3 </math> | ||
Zeile 56: | Zeile 56: | ||
<div align="right"><math>\mathbb{G}=\mathbb{Q}</math></div> | <div align="right"><math>\mathbb{G}=\mathbb{Q}</math></div> | ||
− | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> 12 - 1 = 2x + 1</u> <u style="color:lightgrey;background:lightgrey"> | + | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> 12 - 1 = 2x + 1</u> | <u style="color:lightgrey;background:lightgrey">- 1</u> |
− | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">10 = 2x</u> <u style="color:lightgrey;background:lightgrey"> | + | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">10 = 2x</u> | <u style="color:lightgrey;background:lightgrey">: 2</u> |
:<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">x = 5</u> | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">x = 5</u> | ||
Zeile 82: | Zeile 82: | ||
:<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> 8 + 9 = 5x + 17 </u> | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> 8 + 9 = 5x + 17 </u> | ||
− | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">17 = 5x + 17</u> <u style="color:lightgrey;background:lightgrey"> | + | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">17 = 5x + 17</u> |<u style="color:lightgrey;background:lightgrey"> - 17 </u> |
− | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">0 = 5x</u> <u style="color:lightgrey;background:lightgrey"> | + | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">0 = 5x</u> | <u style="color:lightgrey;background:lightgrey">: 5 </u> |
:<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">x = 0 ... wirklich? </u> | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">x = 0 ... wirklich? </u> | ||
Zeile 108: | Zeile 108: | ||
<div align="right"><math>\mathbb{G}=\mathbb{Q}</math></div> | <div align="right"><math>\mathbb{G}=\mathbb{Q}</math></div> | ||
− | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> 9x + 5 = -13</u> <u style="color:lightgrey;background:lightgrey"> | + | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> 9x + 5 = -13</u> | <u style="color:lightgrey;background:lightgrey">- 5</u> |
− | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">9x = -18</u> <u style="color:lightgrey;background:lightgrey"> | + | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">9x = -18</u> | <u style="color:lightgrey;background:lightgrey">: 9</u> |
:<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">x = -2</u> | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">x = -2</u> | ||
Zeile 133: | Zeile 133: | ||
:<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> -9 + 6x + 2x = -21</u> | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> -9 + 6x + 2x = -21</u> | ||
− | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> -9 + 8x = -21</u> <u style="color:lightgrey;background:lightgrey"> | + | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey"> -9 + 8x = -21</u> | <u style="color:lightgrey;background:lightgrey"> + 9</u> |
− | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">8x = -12</u> <u style="color:lightgrey;background:lightgrey"> | + | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">8x = -12</u> <| u style="color:lightgrey;background:lightgrey">: 8</u> |
:<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">x = -1,5</u> | :<math>\Leftrightarrow</math><u style="color:lightgrey;background:lightgrey">x = -1,5</u> |
Version vom 29. Juni 2009, 15:00 Uhr
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- 3x + 10 = 19 | - 10
- 3x = 9 | : 3
- x = 3
- 9x - 18 = 27 | + 18
- 9x = 45 | : 9
- x = 5
- 12 - 12 : 12 = 2x + 2 : 2
- 12 - 1 = 2x + 1 | - 1
- 10 = 2x | : 2
- x = 5
- 8 + 9 = 5x + 17
- 17 = 5x + 17 | - 17
- 0 = 5x | : 5
- x = 0 ... wirklich?
- 3x + 8 + 6x - 3 = -13
- 9x + 5 = -13 | - 5
- 9x = -18 | : 9
- x = -2
- -9 + 6x + 2x = -21
- -9 + 8x = -21 | + 9
- 8x = -12 <| u style="color:lightgrey;background:lightgrey">: 8</u>
- x = -1,5