Algebra Examples

$3 x + [\begin{array}{c} - 1 & - 2 \\ 10 & - 7 \end{array}] = [\begin{array}{c} - 13 & - 2 \\ - 5 & 14 \end{array}]$

Step 1

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

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Step 1.1

Subtract $[\begin{array}{c} - 1 & - 2 \\ 10 & - 7 \end{array}]$ from both sides of the equation.

$3 x = [\begin{array}{c} - 13 & - 2 \\ - 5 & 14 \end{array}] - [\begin{array}{c} - 1 & - 2 \\ 10 & - 7 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Subtract the corresponding elements.

$3 x = [\begin{array}{c} - 13 + 1 & - 2 + 2 \\ - 5 - 10 & 14 + 7 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Add $- 13$ and $1$ .

$3 x = [\begin{array}{c} - 12 & - 2 + 2 \\ - 5 - 10 & 14 + 7 \end{array}]$

Step 2.2.2

Add $- 2$ and $2$ .

$3 x = [\begin{array}{c} - 12 & 0 \\ - 5 - 10 & 14 + 7 \end{array}]$

Step 2.2.3

Subtract $10$ from $- 5$ .

$3 x = [\begin{array}{c} - 12 & 0 \\ - 15 & 14 + 7 \end{array}]$

Step 2.2.4

Add $14$ and $7$ .

$3 x = [\begin{array}{c} - 12 & 0 \\ - 15 & 21 \end{array}]$

Step 3

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

$\frac{1}{3} (3 x) = \frac{1}{3} [\begin{array}{c} - 12 & 0 \\ - 15 & 21 \end{array}]$

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 $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{1}{3} [\begin{array}{c} - 12 & 0 \\ - 15 & 21 \end{array}]$

Step 4.1.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{1}{3} [\begin{array}{c} - 12 & 0 \\ - 15 & 21 \end{array}]$

Step 4.1.3

Rewrite the expression.

$x = \frac{1}{3} [\begin{array}{c} - 12 & 0 \\ - 15 & 21 \end{array}]$

Step 4.2

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

$x = [\begin{array}{c} \frac{1}{3} \cdot - 12 & \frac{1}{3} \cdot 0 \\ \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 21 \end{array}]$

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 $- 12$ .

$x = [\begin{array}{c} \frac{1}{3} \cdot (3 (- 4)) & \frac{1}{3} \cdot 0 \\ \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 21 \end{array}]$

Step 4.3.1.2

Cancel the common factor.

$x = [\begin{array}{c} \frac{1}{3} \cdot (3 \cdot - 4) & \frac{1}{3} \cdot 0 \\ \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 21 \end{array}]$

Step 4.3.1.3

Rewrite the expression.

$x = [\begin{array}{c} - 4 & \frac{1}{3} \cdot 0 \\ \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 21 \end{array}]$

Step 4.3.2

Multiply $\frac{1}{3}$ by $0$ .

$x = [\begin{array}{c} - 4 & 0 \\ \frac{1}{3} \cdot - 15 & \frac{1}{3} \cdot 21 \end{array}]$

Step 4.3.3

Cancel the common factor of $3$ .

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Step 4.3.3.1

Factor $3$ out of $- 15$ .

$x = [\begin{array}{c} - 4 & 0 \\ \frac{1}{3} \cdot (3 (- 5)) & \frac{1}{3} \cdot 21 \end{array}]$

Step 4.3.3.2

Cancel the common factor.

$x = [\begin{array}{c} - 4 & 0 \\ \frac{1}{3} \cdot (3 \cdot - 5) & \frac{1}{3} \cdot 21 \end{array}]$

Step 4.3.3.3

Rewrite the expression.

$x = [\begin{array}{c} - 4 & 0 \\ - 5 & \frac{1}{3} \cdot 21 \end{array}]$

Step 4.3.4

Cancel the common factor of $3$ .

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Step 4.3.4.1

Factor $3$ out of $21$ .

$x = [\begin{array}{c} - 4 & 0 \\ - 5 & \frac{1}{3} \cdot (3 (7)) \end{array}]$

Step 4.3.4.2

Cancel the common factor.

$x = [\begin{array}{c} - 4 & 0 \\ - 5 & \frac{1}{3} \cdot (3 \cdot 7) \end{array}]$

Step 4.3.4.3

Rewrite the expression.

$x = [\begin{array}{c} - 4 & 0 \\ - 5 & 7 \end{array}]$