Algebra Examples

$- 2 x - [\begin{array}{c} 8 & 4 & 4 \\ 1 & - 5 & - 9 \\ 3 & 2 & 0 \end{array}] = [\begin{array}{c} - 18 & 2 & 22 \\ 9 & - 25 & - 17 \\ 15 & 12 & 10 \end{array}]$

Step 1

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

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Step 1.1

Add $[\begin{array}{c} 8 & 4 & 4 \\ 1 & - 5 & - 9 \\ 3 & 2 & 0 \end{array}]$ to both sides of the equation.

$- 2 x = [\begin{array}{c} - 18 & 2 & 22 \\ 9 & - 25 & - 17 \\ 15 & 12 & 10 \end{array}] + [\begin{array}{c} 8 & 4 & 4 \\ 1 & - 5 & - 9 \\ 3 & 2 & 0 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Add the corresponding elements.

$- 2 x = [\begin{array}{c} - 18 + 8 & 2 + 4 & 22 + 4 \\ 9 + 1 & - 25 - 5 & - 17 - 9 \\ 15 + 3 & 12 + 2 & 10 + 0 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Add $- 18$ and $8$ .

$- 2 x = [\begin{array}{c} - 10 & 2 + 4 & 22 + 4 \\ 9 + 1 & - 25 - 5 & - 17 - 9 \\ 15 + 3 & 12 + 2 & 10 + 0 \end{array}]$

Step 2.2.2

Add $2$ and $4$ .

$- 2 x = [\begin{array}{c} - 10 & 6 & 22 + 4 \\ 9 + 1 & - 25 - 5 & - 17 - 9 \\ 15 + 3 & 12 + 2 & 10 + 0 \end{array}]$

Step 2.2.3

Add $22$ and $4$ .

$- 2 x = [\begin{array}{c} - 10 & 6 & 26 \\ 9 + 1 & - 25 - 5 & - 17 - 9 \\ 15 + 3 & 12 + 2 & 10 + 0 \end{array}]$

Step 2.2.4

Add $9$ and $1$ .

$- 2 x = [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 25 - 5 & - 17 - 9 \\ 15 + 3 & 12 + 2 & 10 + 0 \end{array}]$

Step 2.2.5

Subtract $5$ from $- 25$ .

$- 2 x = [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 17 - 9 \\ 15 + 3 & 12 + 2 & 10 + 0 \end{array}]$

Step 2.2.6

Subtract $9$ from $- 17$ .

$- 2 x = [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 15 + 3 & 12 + 2 & 10 + 0 \end{array}]$

Step 2.2.7

Add $15$ and $3$ .

$- 2 x = [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 12 + 2 & 10 + 0 \end{array}]$

Step 2.2.8

Add $12$ and $2$ .

$- 2 x = [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 14 & 10 + 0 \end{array}]$

Step 2.2.9

Add $10$ and $0$ .

$- 2 x = [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 14 & 10 \end{array}]$

Step 3

Multiply both sides by $- \frac{1}{2}$ .

$- \frac{1}{2} (- 2 x) = - \frac{1}{2} [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 14 & 10 \end{array}]$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} (- 2 x) = - \frac{1}{2} [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 14 & 10 \end{array}]$

Step 4.1.2

Factor $2$ out of $- 2 x$ .

$\frac{- 1}{2} (2 (- x)) = - \frac{1}{2} [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 14 & 10 \end{array}]$

Step 4.1.3

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{1}{2} [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 14 & 10 \end{array}]$

Step 4.1.4

Rewrite the expression.

$- - x = - \frac{1}{2} [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 14 & 10 \end{array}]$

Step 4.2

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{1}{2} [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 14 & 10 \end{array}]$

Step 4.3

Multiply $x$ by $1$ .

$x = - \frac{1}{2} [\begin{array}{c} - 10 & 6 & 26 \\ 10 & - 30 & - 26 \\ 18 & 14 & 10 \end{array}]$

Step 4.4

Multiply $- \frac{1}{2}$ by each element of the matrix.

$x = [\begin{array}{c} - \frac{1}{2} \cdot - 10 & - \frac{1}{2} \cdot 6 & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5

Simplify each element in the matrix.

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Step 4.5.1

Cancel the common factor of $2$ .

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Step 4.5.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} \frac{- 1}{2} \cdot - 10 & - \frac{1}{2} \cdot 6 & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.1.2

Factor $2$ out of $- 10$ .

$x = [\begin{array}{c} \frac{- 1}{2} \cdot (2 (- 5)) & - \frac{1}{2} \cdot 6 & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.1.3

Cancel the common factor.

$x = [\begin{array}{c} \frac{- 1}{2} \cdot (2 \cdot - 5) & - \frac{1}{2} \cdot 6 & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.1.4

Rewrite the expression.

$x = [\begin{array}{c} - 1 \cdot - 5 & - \frac{1}{2} \cdot 6 & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.2

Multiply $- 1$ by $- 5$ .

$x = [\begin{array}{c} 5 & - \frac{1}{2} \cdot 6 & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.3

Cancel the common factor of $2$ .

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Step 4.5.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} 5 & \frac{- 1}{2} \cdot 6 & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.3.2

Factor $2$ out of $6$ .

$x = [\begin{array}{c} 5 & \frac{- 1}{2} \cdot (2 (3)) & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.3.3

Cancel the common factor.

$x = [\begin{array}{c} 5 & \frac{- 1}{2} \cdot (2 \cdot 3) & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.3.4

Rewrite the expression.

$x = [\begin{array}{c} 5 & - 1 \cdot 3 & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.4

Multiply $- 1$ by $3$ .

$x = [\begin{array}{c} 5 & - 3 & - \frac{1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.5

Cancel the common factor of $2$ .

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Step 4.5.5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} 5 & - 3 & \frac{- 1}{2} \cdot 26 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.5.2

Factor $2$ out of $26$ .

$x = [\begin{array}{c} 5 & - 3 & \frac{- 1}{2} \cdot (2 (13)) \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.5.3

Cancel the common factor.

$x = [\begin{array}{c} 5 & - 3 & \frac{- 1}{2} \cdot (2 \cdot 13) \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.5.4

Rewrite the expression.

$x = [\begin{array}{c} 5 & - 3 & - 1 \cdot 13 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.6

Multiply $- 1$ by $13$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - \frac{1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.7

Cancel the common factor of $2$ .

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Step 4.5.7.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ \frac{- 1}{2} \cdot 10 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.7.2

Factor $2$ out of $10$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ \frac{- 1}{2} \cdot (2 (5)) & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.7.3

Cancel the common factor.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ \frac{- 1}{2} \cdot (2 \cdot 5) & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.7.4

Rewrite the expression.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 1 \cdot 5 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.8

Multiply $- 1$ by $5$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & - \frac{1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.9

Cancel the common factor of $2$ .

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Step 4.5.9.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & \frac{- 1}{2} \cdot - 30 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.9.2

Factor $2$ out of $- 30$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & \frac{- 1}{2} \cdot (2 (- 15)) & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.9.3

Cancel the common factor.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & \frac{- 1}{2} \cdot (2 \cdot - 15) & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.9.4

Rewrite the expression.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & - 1 \cdot - 15 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.10

Multiply $- 1$ by $- 15$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & - \frac{1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.11

Cancel the common factor of $2$ .

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Step 4.5.11.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & \frac{- 1}{2} \cdot - 26 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.11.2

Factor $2$ out of $- 26$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & \frac{- 1}{2} \cdot (2 (- 13)) \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.11.3

Cancel the common factor.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & \frac{- 1}{2} \cdot (2 \cdot - 13) \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.11.4

Rewrite the expression.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & - 1 \cdot - 13 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.12

Multiply $- 1$ by $- 13$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - \frac{1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.13

Cancel the common factor of $2$ .

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Step 4.5.13.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ \frac{- 1}{2} \cdot 18 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.13.2

Factor $2$ out of $18$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ \frac{- 1}{2} \cdot (2 (9)) & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.13.3

Cancel the common factor.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ \frac{- 1}{2} \cdot (2 \cdot 9) & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.13.4

Rewrite the expression.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 1 \cdot 9 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.14

Multiply $- 1$ by $9$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & - \frac{1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.15

Cancel the common factor of $2$ .

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Step 4.5.15.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & \frac{- 1}{2} \cdot 14 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.15.2

Factor $2$ out of $14$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & \frac{- 1}{2} \cdot (2 (7)) & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.15.3

Cancel the common factor.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & \frac{- 1}{2} \cdot (2 \cdot 7) & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.15.4

Rewrite the expression.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & - 1 \cdot 7 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.16

Multiply $- 1$ by $7$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & - 7 & - \frac{1}{2} \cdot 10 \end{array}]$

Step 4.5.17

Cancel the common factor of $2$ .

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Step 4.5.17.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & - 7 & \frac{- 1}{2} \cdot 10 \end{array}]$

Step 4.5.17.2

Factor $2$ out of $10$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & - 7 & \frac{- 1}{2} \cdot (2 (5)) \end{array}]$

Step 4.5.17.3

Cancel the common factor.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & - 7 & \frac{- 1}{2} \cdot (2 \cdot 5) \end{array}]$

Step 4.5.17.4

Rewrite the expression.

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & - 7 & - 1 \cdot 5 \end{array}]$

Step 4.5.18

Multiply $- 1$ by $5$ .

$x = [\begin{array}{c} 5 & - 3 & - 13 \\ - 5 & 15 & 13 \\ - 9 & - 7 & - 5 \end{array}]$