Algebra Examples

$2 X + 2 [\begin{array}{c} 2 & - 8 \\ - 4 & 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1

Simplify each term.

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Step 1.1

Multiply $2$ by each element of the matrix.

$2 X + [\begin{array}{c} 2 \cdot 2 & 2 \cdot - 8 \\ 2 \cdot - 4 & 2 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $2$ by $2$ .

$2 X + [\begin{array}{c} 4 & 2 \cdot - 8 \\ 2 \cdot - 4 & 2 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.2

Multiply $2$ by $- 8$ .

$2 X + [\begin{array}{c} 4 & - 16 \\ 2 \cdot - 4 & 2 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.3

Multiply $2$ by $- 4$ .

$2 X + [\begin{array}{c} 4 & - 16 \\ - 8 & 2 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.4

Multiply $2$ by $2$ .

$2 X + [\begin{array}{c} 4 & - 16 \\ - 8 & 4 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2

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

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Step 2.1

Subtract $[\begin{array}{c} 4 & - 16 \\ - 8 & 4 \end{array}]$ from both sides of the equation.

$2 X = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} 4 & - 16 \\ - 8 & 4 \end{array}]$

Step 3

Simplify the right side.

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Step 3.1

Subtract the corresponding elements.

$2 X = [\begin{array}{c} 4 - 4 & - 6 + 16 \\ 2 + 8 & - 8 - 4 \end{array}]$

Step 3.2

Simplify each element.

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Step 3.2.1

Subtract $4$ from $4$ .

$2 X = [\begin{array}{c} 0 & - 6 + 16 \\ 2 + 8 & - 8 - 4 \end{array}]$

Step 3.2.2

Add $- 6$ and $16$ .

$2 X = [\begin{array}{c} 0 & 10 \\ 2 + 8 & - 8 - 4 \end{array}]$

Step 3.2.3

Add $2$ and $8$ .

$2 X = [\begin{array}{c} 0 & 10 \\ 10 & - 8 - 4 \end{array}]$

Step 3.2.4

Subtract $4$ from $- 8$ .

$2 X = [\begin{array}{c} 0 & 10 \\ 10 & - 12 \end{array}]$

Step 4

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

$\frac{1}{2} (2 X) = \frac{1}{2} [\begin{array}{c} 0 & 10 \\ 10 & - 12 \end{array}]$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $2$ .

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Step 5.1.1

Factor $2$ out of $2 X$ .

$\frac{1}{2} (2 (X)) = \frac{1}{2} [\begin{array}{c} 0 & 10 \\ 10 & - 12 \end{array}]$

Step 5.1.2

Cancel the common factor.

$\frac{1}{2} (2 X) = \frac{1}{2} [\begin{array}{c} 0 & 10 \\ 10 & - 12 \end{array}]$

Step 5.1.3

Rewrite the expression.

$X = \frac{1}{2} [\begin{array}{c} 0 & 10 \\ 10 & - 12 \end{array}]$

Step 5.2

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

$X = [\begin{array}{c} \frac{1}{2} \cdot 0 & \frac{1}{2} \cdot 10 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot - 12 \end{array}]$

Step 5.3

Simplify each element in the matrix.

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Step 5.3.1

Multiply $\frac{1}{2}$ by $0$ .

$X = [\begin{array}{c} 0 & \frac{1}{2} \cdot 10 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot - 12 \end{array}]$

Step 5.3.2

Cancel the common factor of $2$ .

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Step 5.3.2.1

Factor $2$ out of $10$ .

$X = [\begin{array}{c} 0 & \frac{1}{2} \cdot (2 (5)) \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot - 12 \end{array}]$

Step 5.3.2.2

Cancel the common factor.

$X = [\begin{array}{c} 0 & \frac{1}{2} \cdot (2 \cdot 5) \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot - 12 \end{array}]$

Step 5.3.2.3

Rewrite the expression.

$X = [\begin{array}{c} 0 & 5 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot - 12 \end{array}]$

Step 5.3.3

Cancel the common factor of $2$ .

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Step 5.3.3.1

Factor $2$ out of $10$ .

$X = [\begin{array}{c} 0 & 5 \\ \frac{1}{2} \cdot (2 (5)) & \frac{1}{2} \cdot - 12 \end{array}]$

Step 5.3.3.2

Cancel the common factor.

$X = [\begin{array}{c} 0 & 5 \\ \frac{1}{2} \cdot (2 \cdot 5) & \frac{1}{2} \cdot - 12 \end{array}]$

Step 5.3.3.3

Rewrite the expression.

$X = [\begin{array}{c} 0 & 5 \\ 5 & \frac{1}{2} \cdot - 12 \end{array}]$

Step 5.3.4

Cancel the common factor of $2$ .

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Step 5.3.4.1

Factor $2$ out of $- 12$ .

$X = [\begin{array}{c} 0 & 5 \\ 5 & \frac{1}{2} \cdot (2 (- 6)) \end{array}]$

Step 5.3.4.2

Cancel the common factor.

$X = [\begin{array}{c} 0 & 5 \\ 5 & \frac{1}{2} \cdot (2 \cdot - 6) \end{array}]$

Step 5.3.4.3

Rewrite the expression.

$X = [\begin{array}{c} 0 & 5 \\ 5 & - 6 \end{array}]$