Algebra Examples

$- 4 [\begin{array}{c} - 1 & 3 \\ 5 & - 2 \\ 6 & 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}] = - 5 x$

Step 1

Multiply $- 4$ by each element of the matrix.

$- 5 x = [\begin{array}{c} - 4 \cdot - 1 & - 4 \cdot 3 \\ - 4 \cdot 5 & - 4 \cdot - 2 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}]$

Step 2

Simplify each element in the matrix.

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Rearrange $- 4 \cdot - 1$ .

$- 5 x = [\begin{array}{c} 4 & - 4 \cdot 3 \\ - 4 \cdot 5 & - 4 \cdot - 2 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}]$

Rearrange $- 4 \cdot 3$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 4 \cdot 5 & - 4 \cdot - 2 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}]$

Rearrange $- 4 \cdot 5$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & - 4 \cdot - 2 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}]$

Rearrange $- 4 \cdot - 2$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}]$

Rearrange $- 4 \cdot 6$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}]$

Rearrange $- 4 \cdot 5$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}]$

Step 3

Multiply $- 2$ by each element of the matrix.

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} - 2 \cdot - 9 & - 2 \cdot 0 \\ - 2 \cdot - 2 & - 2 \cdot 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}]$

Step 4

Simplify each element in the matrix.

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Rearrange $- 2 \cdot - 9$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & - 2 \cdot 0 \\ - 2 \cdot - 2 & - 2 \cdot 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}]$

Rearrange $- 2 \cdot 0$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ - 2 \cdot - 2 & - 2 \cdot 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}]$

Rearrange $- 2 \cdot - 2$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ 4 & - 2 \cdot 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}]$

Rearrange $- 2 \cdot 0$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ 4 & 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}]$

Rearrange $- 2 \cdot 5$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ 4 & 0 \\ - 10 & - 2 \cdot - 4 \end{array}]$

Rearrange $- 2 \cdot - 4$ .

$- 5 x = [\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ 4 & 0 \\ - 10 & 8 \end{array}]$

Step 5

Simplify the right side of the equation.

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Add the corresponding elements.

$- 5 X = [\begin{array}{c} 4 + 18 & - 12 + 0 \\ - 20 + 4 & 8 + 0 \\ - 24 - 10 & - 20 + 8 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 4 + 18 & - 12 + 0 \\ - 20 + 4 & 8 + 0 \\ - 24 - 10 & - 20 + 8 \end{array}]$ .

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Simplify $4 + 18$ .

$- 5 X = [\begin{array}{c} 22 & - 12 + 0 \\ - 20 + 4 & 8 + 0 \\ - 24 - 10 & - 20 + 8 \end{array}]$

Simplify $- 12 + 0$ .

$- 5 X = [\begin{array}{c} 22 & - 12 \\ - 20 + 4 & 8 + 0 \\ - 24 - 10 & - 20 + 8 \end{array}]$

Simplify $- 20 + 4$ .

$- 5 X = [\begin{array}{c} 22 & - 12 \\ - 16 & 8 + 0 \\ - 24 - 10 & - 20 + 8 \end{array}]$

Simplify $8 + 0$ .

$- 5 X = [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 24 - 10 & - 20 + 8 \end{array}]$

Simplify $- 24 - 10$ .

$- 5 X = [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 34 & - 20 + 8 \end{array}]$

Simplify $- 20 + 8$ .

$- 5 X = [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 34 & - 12 \end{array}]$

Step 6

Multiply both sides of the equation by $- \frac{1}{5}$ .

$- \frac{1}{5} \cdot (- 5 X) = - \frac{1}{5} \cdot [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 34 & - 12 \end{array}]$

Step 7

Simplify both sides of the equation.

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Simplify the left side of the equation.

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Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{1}{5}$ into the numerator.

$\frac{- 1}{5} \cdot (- 5 X) = - \frac{1}{5} \cdot [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 34 & - 12 \end{array}]$

Factor $5$ out of $- 5 X$ .

$\frac{- 1}{5} \cdot (5 (- X)) = - \frac{1}{5} \cdot [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 34 & - 12 \end{array}]$

Cancel the common factor.

$\frac{- 1}{5} \cdot (5 (- X)) = - \frac{1}{5} \cdot [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 34 & - 12 \end{array}]$

Rewrite the expression.

$- 1 \cdot (- X) = - \frac{1}{5} \cdot [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 34 & - 12 \end{array}]$

Multiply.

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Multiply $- 1$ by $- 1$ .

$1 \cdot X = - \frac{1}{5} \cdot [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 34 & - 12 \end{array}]$

Multiply $X$ by $1$ .

$X = - \frac{1}{5} \cdot [\begin{array}{c} 22 & - 12 \\ - 16 & 8 \\ - 34 & - 12 \end{array}]$

Simplify the right side of the equation.

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Multiply $- \frac{1}{5}$ by each element of the matrix.

$X = [\begin{array}{c} - \frac{1}{5} \cdot 22 & - \frac{1}{5} \cdot - 12 \\ - \frac{1}{5} \cdot - 16 & - \frac{1}{5} \cdot 8 \\ - \frac{1}{5} \cdot - 34 & - \frac{1}{5} \cdot - 12 \end{array}]$

Simplify each element in the matrix.

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Rearrange $- \frac{1}{5} \cdot 22$ .

$X = [\begin{array}{c} - \frac{22}{5} & - \frac{1}{5} \cdot - 12 \\ - \frac{1}{5} \cdot - 16 & - \frac{1}{5} \cdot 8 \\ - \frac{1}{5} \cdot - 34 & - \frac{1}{5} \cdot - 12 \end{array}]$

Rearrange $- \frac{1}{5} \cdot - 12$ .

$X = [\begin{array}{c} - \frac{22}{5} & \frac{12}{5} \\ - \frac{1}{5} \cdot - 16 & - \frac{1}{5} \cdot 8 \\ - \frac{1}{5} \cdot - 34 & - \frac{1}{5} \cdot - 12 \end{array}]$

Rearrange $- \frac{1}{5} \cdot - 16$ .

$X = [\begin{array}{c} - \frac{22}{5} & \frac{12}{5} \\ \frac{16}{5} & - \frac{1}{5} \cdot 8 \\ - \frac{1}{5} \cdot - 34 & - \frac{1}{5} \cdot - 12 \end{array}]$

Rearrange $- \frac{1}{5} \cdot 8$ .

$X = [\begin{array}{c} - \frac{22}{5} & \frac{12}{5} \\ \frac{16}{5} & - \frac{8}{5} \\ - \frac{1}{5} \cdot - 34 & - \frac{1}{5} \cdot - 12 \end{array}]$

Rearrange $- \frac{1}{5} \cdot - 34$ .

$X = [\begin{array}{c} - \frac{22}{5} & \frac{12}{5} \\ \frac{16}{5} & - \frac{8}{5} \\ \frac{34}{5} & - \frac{1}{5} \cdot - 12 \end{array}]$

Rearrange $- \frac{1}{5} \cdot - 12$ .

$X = [\begin{array}{c} - \frac{22}{5} & \frac{12}{5} \\ \frac{16}{5} & - \frac{8}{5} \\ \frac{34}{5} & \frac{12}{5} \end{array}]$

Step 8

Multiply $- 4$ by each element of the matrix.

$[\begin{array}{c} - 4 \cdot - 1 & - 4 \cdot 3 \\ - 4 \cdot 5 & - 4 \cdot - 2 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}] = - 5 x$

Step 9

Simplify each element in the matrix.

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Rearrange $- 4 \cdot - 1$ .

$[\begin{array}{c} 4 & - 4 \cdot 3 \\ - 4 \cdot 5 & - 4 \cdot - 2 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}] = - 5 x$

Rearrange $- 4 \cdot 3$ .

$[\begin{array}{c} 4 & - 12 \\ - 4 \cdot 5 & - 4 \cdot - 2 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}] = - 5 x$

Rearrange $- 4 \cdot 5$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & - 4 \cdot - 2 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}] = - 5 x$

Rearrange $- 4 \cdot - 2$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 4 \cdot 6 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}] = - 5 x$

Rearrange $- 4 \cdot 6$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 4 \cdot 5 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}] = - 5 x$

Rearrange $- 4 \cdot 5$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] - 2 [\begin{array}{c} - 9 & 0 \\ - 2 & 0 \\ 5 & - 4 \end{array}] = - 5 x$

Step 10

Multiply $- 2$ by each element of the matrix.

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} - 2 \cdot - 9 & - 2 \cdot 0 \\ - 2 \cdot - 2 & - 2 \cdot 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}] = - 5 x$

Step 11

Simplify each element in the matrix.

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Rearrange $- 2 \cdot - 9$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & - 2 \cdot 0 \\ - 2 \cdot - 2 & - 2 \cdot 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}] = - 5 x$

Rearrange $- 2 \cdot 0$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ - 2 \cdot - 2 & - 2 \cdot 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}] = - 5 x$

Rearrange $- 2 \cdot - 2$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ 4 & - 2 \cdot 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}] = - 5 x$

Rearrange $- 2 \cdot 0$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ 4 & 0 \\ - 2 \cdot 5 & - 2 \cdot - 4 \end{array}] = - 5 x$

Rearrange $- 2 \cdot 5$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ 4 & 0 \\ - 10 & - 2 \cdot - 4 \end{array}] = - 5 x$

Rearrange $- 2 \cdot - 4$ .

$[\begin{array}{c} 4 & - 12 \\ - 20 & 8 \\ - 24 & - 20 \end{array}] + [\begin{array}{c} 18 & 0 \\ 4 & 0 \\ - 10 & 8 \end{array}] = - 5 x$

Step 12

The table does not have enough points.

The table does not have a function rule.