Algebra Beispiele

x - [\begin{array}{c} 1 & - 12 & 0 \\ 10 & 9 & 1 \end{array}] = [\begin{array}{c} - 2 & 12 & 2 \\ - 8 & \frac{3}{2} & 4 \end{array}]

$x - [\begin{array}{c} 1 & - 12 & 0 \\ 10 & 9 & 1 \end{array}] = [\begin{array}{c} - 2 & 12 & 2 \\ - 8 & \frac{3}{2} & 4 \end{array}]$

Schritt 1

Move all terms not containing a variable to the right side.

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Schritt 1.1

Addiere

[\begin{array}{c} 1 & - 12 & 0 \\ 10 & 9 & 1 \end{array}]

$[\begin{array}{c} 1 & - 12 & 0 \\ 10 & 9 & 1 \end{array}]$ zu beiden Seiten der Gleichung.

x = [\begin{array}{c} - 2 & 12 & 2 \\ - 8 & \frac{3}{2} & 4 \end{array}] + [\begin{array}{c} 1 & - 12 & 0 \\ 10 & 9 & 1 \end{array}]

$x = [\begin{array}{c} - 2 & 12 & 2 \\ - 8 & \frac{3}{2} & 4 \end{array}] + [\begin{array}{c} 1 & - 12 & 0 \\ 10 & 9 & 1 \end{array}]$

x = [\begin{array}{c} - 2 & 12 & 2 \\ - 8 & \frac{3}{2} & 4 \end{array}] + [\begin{array}{c} 1 & - 12 & 0 \\ 10 & 9 & 1 \end{array}]

$x = [\begin{array}{c} - 2 & 12 & 2 \\ - 8 & \frac{3}{2} & 4 \end{array}] + [\begin{array}{c} 1 & - 12 & 0 \\ 10 & 9 & 1 \end{array}]$

Schritt 2

Vereinfache die rechte Seite.

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Schritt 2.1

Addiere die entsprechenden Elemente.

x = [\begin{array}{c} - 2 + 1 & 12 - 12 & 2 + 0 \\ - 8 + 10 & \frac{3}{2} + 9 & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 2 + 1 & 12 - 12 & 2 + 0 \\ - 8 + 10 & \frac{3}{2} + 9 & 4 + 1 \end{array}]$

Schritt 2.2

Simplify each element.

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Schritt 2.2.1

Addiere

- 2

$- 2$ und

1

$1$ .

x = [\begin{array}{c} - 1 & 12 - 12 & 2 + 0 \\ - 8 + 10 & \frac{3}{2} + 9 & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 12 - 12 & 2 + 0 \\ - 8 + 10 & \frac{3}{2} + 9 & 4 + 1 \end{array}]$

Schritt 2.2.2

Subtrahiere

12

$12$ von

12

$12$ .

x = [\begin{array}{c} - 1 & 0 & 2 + 0 \\ - 8 + 10 & \frac{3}{2} + 9 & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 + 0 \\ - 8 + 10 & \frac{3}{2} + 9 & 4 + 1 \end{array}]$

Schritt 2.2.3

Addiere

2

$2$ und

0

$0$ .

x = [\begin{array}{c} - 1 & 0 & 2 \\ - 8 + 10 & \frac{3}{2} + 9 & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ - 8 + 10 & \frac{3}{2} + 9 & 4 + 1 \end{array}]$

Schritt 2.2.4

Addiere

- 8

$- 8$ und

10

$10$ .

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3}{2} + 9 & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3}{2} + 9 & 4 + 1 \end{array}]$

Schritt 2.2.5

9

$9$ als Bruch mit einem gemeinsamen Nenner zu schreiben, multipliziere mit

\frac{2}{2}

$\frac{2}{2}$ .

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3}{2} + 9 \cdot \frac{2}{2} & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3}{2} + 9 \cdot \frac{2}{2} & 4 + 1 \end{array}]$

Schritt 2.2.6

Kombiniere

9

$9$ und

\frac{2}{2}

$\frac{2}{2}$ .

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3}{2} + \frac{9 \cdot 2}{2} & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3}{2} + \frac{9 \cdot 2}{2} & 4 + 1 \end{array}]$

Schritt 2.2.7

Vereinige die Zähler über dem gemeinsamen Nenner.

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3 + 9 \cdot 2}{2} & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3 + 9 \cdot 2}{2} & 4 + 1 \end{array}]$

Schritt 2.2.8

Vereinfache den Zähler.

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Schritt 2.2.8.1

Mutltipliziere

9

$9$ mit

2

$2$ .

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3 + 18}{2} & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{3 + 18}{2} & 4 + 1 \end{array}]$

Schritt 2.2.8.2

Addiere

3

$3$ und

18

$18$ .

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 4 + 1 \end{array}]$

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 4 + 1 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 4 + 1 \end{array}]$

Schritt 2.2.9

Addiere

4

$4$ und

1

$1$ .

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 5 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 5 \end{array}]$

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 5 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 5 \end{array}]$

x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 5 \end{array}]

$x = [\begin{array}{c} - 1 & 0 & 2 \\ 2 & \frac{21}{2} & 5 \end{array}]$

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