Algebra Examples

$3 x + [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}] = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}]$

Step 1

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

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Step 1.1

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

$3 x = [\begin{array}{c} 11 & 4 & 9 \\ 2 & - 17 & 0 \\ - 14 & - 12 & 5 \end{array}] - [\begin{array}{c} - 1 & 1 & 0 \\ 8 & - 5 & 9 \\ 4 & 3 & - 1 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Subtract the corresponding elements.

$3 x = [\begin{array}{c} 11 + 1 & 4 - 1 & 9 - 0 \\ 2 - 8 & - 17 + 5 & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 + 1 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Add $11$ and $1$ .

$3 x = [\begin{array}{c} 12 & 4 - 1 & 9 - 0 \\ 2 - 8 & - 17 + 5 & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 + 1 \end{array}]$

Step 2.2.2

Subtract $1$ from $4$ .

$3 x = [\begin{array}{c} 12 & 3 & 9 - 0 \\ 2 - 8 & - 17 + 5 & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 + 1 \end{array}]$

Step 2.2.3

Subtract $0$ from $9$ .

$3 x = [\begin{array}{c} 12 & 3 & 9 \\ 2 - 8 & - 17 + 5 & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 + 1 \end{array}]$

Step 2.2.4

Subtract $8$ from $2$ .

$3 x = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 17 + 5 & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 + 1 \end{array}]$

Step 2.2.5

Add $- 17$ and $5$ .

$3 x = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & 0 - 9 \\ - 14 - 4 & - 12 - 3 & 5 + 1 \end{array}]$

Step 2.2.6

Subtract $9$ from $0$ .

$3 x = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 14 - 4 & - 12 - 3 & 5 + 1 \end{array}]$

Step 2.2.7

Subtract $4$ from $- 14$ .

$3 x = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 12 - 3 & 5 + 1 \end{array}]$

Step 2.2.8

Subtract $3$ from $- 12$ .

$3 x = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 5 + 1 \end{array}]$

Step 2.2.9

Add $5$ and $1$ .

$3 x = [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Step 3

Multiply both sides by $\frac{1}{3}$ .

$\frac{1}{3} (3 x) = \frac{1}{3} [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Step 4

Simplify.

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Step 4.1

Cancel the common factor of $3$ .

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Step 4.1.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{1}{3} [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Step 4.1.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{1}{3} [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Step 4.1.3

Rewrite the expression.

$x = \frac{1}{3} [\begin{array}{c} 12 & 3 & 9 \\ - 6 & - 12 & - 9 \\ - 18 & - 15 & 6 \end{array}]$

Step 4.2

Multiply $\frac{1}{3}$ by each element of the matrix.

$x = [\begin{array}{c} \frac{1}{3} \cdot 12 & \frac{1}{3} \cdot 3 & \frac{1}{3} \cdot 9 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3

Simplify each element in the matrix.

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Step 4.3.1

Cancel the common factor of $3$ .

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Step 4.3.1.1

Factor $3$ out of $12$ .

$x = [\begin{array}{c} \frac{1}{3} \cdot (3 (4)) & \frac{1}{3} \cdot 3 & \frac{1}{3} \cdot 9 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.1.2

Cancel the common factor.

$x = [\begin{array}{c} \frac{1}{3} \cdot (3 \cdot 4) & \frac{1}{3} \cdot 3 & \frac{1}{3} \cdot 9 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.1.3

Rewrite the expression.

$x = [\begin{array}{c} 4 & \frac{1}{3} \cdot 3 & \frac{1}{3} \cdot 9 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.2

Cancel the common factor of $3$ .

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Step 4.3.2.1

Cancel the common factor.

Step 4.3.2.2

Rewrite the expression.

$x = [\begin{array}{c} 4 & 1 & \frac{1}{3} \cdot 9 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.3

Cancel the common factor of $3$ .

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Step 4.3.3.1

Factor $3$ out of $9$ .

$x = [\begin{array}{c} 4 & 1 & \frac{1}{3} \cdot (3 (3)) \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.3.2

Cancel the common factor.

$x = [\begin{array}{c} 4 & 1 & \frac{1}{3} \cdot (3 \cdot 3) \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.3.3

Rewrite the expression.

$x = [\begin{array}{c} 4 & 1 & 3 \\ \frac{1}{3} \cdot - 6 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.4

Cancel the common factor of $3$ .

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Step 4.3.4.1

Factor $3$ out of $- 6$ .

$x = [\begin{array}{c} 4 & 1 & 3 \\ \frac{1}{3} \cdot (3 (- 2)) & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.4.2

Cancel the common factor.

$x = [\begin{array}{c} 4 & 1 & 3 \\ \frac{1}{3} \cdot (3 \cdot - 2) & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.4.3

Rewrite the expression.

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.5

Cancel the common factor of $3$ .

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Step 4.3.5.1

Factor $3$ out of $- 12$ .

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & \frac{1}{3} \cdot (3 (- 4)) & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.5.2

Cancel the common factor.

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & \frac{1}{3} \cdot (3 \cdot - 4) & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.5.3

Rewrite the expression.

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & \frac{1}{3} \cdot - 9 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.6

Cancel the common factor of $3$ .

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Step 4.3.6.1

Factor $3$ out of $- 9$ .

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & \frac{1}{3} \cdot (3 (- 3)) \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.6.2

Cancel the common factor.

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & \frac{1}{3} \cdot (3 \cdot - 3) \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.6.3

Rewrite the expression.

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & - 3 \\ \frac{1}{3} \cdot - 18 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.7

Cancel the common factor of $3$ .

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Step 4.3.7.1

Factor $3$ out of $- 18$ .

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & - 3 \\ \frac{1}{3} \cdot (3 (- 6)) & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.7.2

Cancel the common factor.

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & - 3 \\ \frac{1}{3} \cdot (3 \cdot - 6) & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.7.3

Rewrite the expression.

$x = [\begin{array}{c} 4 & 1 & 3 \\ - 2 & - 4 & - 3 \\ - 6 & \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 6 \end{array}]$

Step 4.3.8

Cancel the common factor of $3$ .

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Step 4.3.8.1

Factor $3$ out of $- 15$ .

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

Step 4.3.8.2

Cancel the common factor.

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

Step 4.3.8.3

Rewrite the expression.

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

Step 4.3.9

Cancel the common factor of $3$ .

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Step 4.3.9.1

Factor $3$ out of $6$ .

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

Step 4.3.9.2

Cancel the common factor.

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

Step 4.3.9.3

Rewrite the expression.

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