Algebra Examples

2 x = [\begin{matrix} 4 & 12 1 & - 4 \end{matrix}] + [\begin{matrix} - 2 & 0 3 & 4 \end{matrix}]

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

Step 1

Simplify the right side of the equation.

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Add the corresponding elements.

2 X = [\begin{matrix} 4 - 2 & 12 + 0 1 + 3 & - 4 + 4 \end{matrix}]

$2 X = [\begin{array}{c} 4 - 2 & 12 + 0 \\ 1 + 3 & - 4 + 4 \end{array}]$

Simplify each element of the matrix

[\begin{matrix} 4 - 2 & 12 + 0 1 + 3 & - 4 + 4 \end{matrix}]

$[\begin{array}{c} 4 - 2 & 12 + 0 \\ 1 + 3 & - 4 + 4 \end{array}]$ .

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Simplify

4 - 2

$4 - 2$ .

2 X = [\begin{matrix} 2 & 12 + 0 1 + 3 & - 4 + 4 \end{matrix}]

$2 X = [\begin{array}{c} 2 & 12 + 0 \\ 1 + 3 & - 4 + 4 \end{array}]$

Simplify

12 + 0

$12 + 0$ .

2 X = [\begin{matrix} 2 & 12 1 + 3 & - 4 + 4 \end{matrix}]

$2 X = [\begin{array}{c} 2 & 12 \\ 1 + 3 & - 4 + 4 \end{array}]$

Simplify

1 + 3

$1 + 3$ .

2 X = [\begin{matrix} 2 & 12 4 & - 4 + 4 \end{matrix}]

$2 X = [\begin{array}{c} 2 & 12 \\ 4 & - 4 + 4 \end{array}]$

Simplify

- 4 + 4

$- 4 + 4$ .

2 X = [\begin{matrix} 2 & 12 4 & 0 \end{matrix}]

$2 X = [\begin{array}{c} 2 & 12 \\ 4 & 0 \end{array}]$

2 X = [\begin{matrix} 2 & 12 4 & 0 \end{matrix}]

$2 X = [\begin{array}{c} 2 & 12 \\ 4 & 0 \end{array}]$

2 X = [\begin{matrix} 2 & 12 4 & 0 \end{matrix}]

$2 X = [\begin{array}{c} 2 & 12 \\ 4 & 0 \end{array}]$

Step 2

Multiply both sides of the equation by

\frac{1}{2}

$\frac{1}{2}$ .

\frac{1}{2} \cdot (2 X) = \frac{1}{2} \cdot [\begin{matrix} 2 & 12 4 & 0 \end{matrix}]

$\frac{1}{2} \cdot (2 X) = \frac{1}{2} \cdot [\begin{array}{c} 2 & 12 \\ 4 & 0 \end{array}]$

Step 3

Simplify both sides of the equation.

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Cancel the common factor of

2

$2$ .

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Factor

2

$2$ out of

2 X

$2 X$ .

\frac{1}{2} \cdot (2 (X)) = \frac{1}{2} \cdot [\begin{matrix} 2 & 12 4 & 0 \end{matrix}]

$\frac{1}{2} \cdot (2 (X)) = \frac{1}{2} \cdot [\begin{array}{c} 2 & 12 \\ 4 & 0 \end{array}]$

Cancel the common factor.

\frac{1}{2} \cdot (2 X) = \frac{1}{2} \cdot [\begin{matrix} 2 & 12 4 & 0 \end{matrix}]

$\frac{1}{2} \cdot (2 X) = \frac{1}{2} \cdot [\begin{array}{c} 2 & 12 \\ 4 & 0 \end{array}]$

Rewrite the expression.

X = \frac{1}{2} \cdot [\begin{matrix} 2 & 12 4 & 0 \end{matrix}]

$X = \frac{1}{2} \cdot [\begin{array}{c} 2 & 12 \\ 4 & 0 \end{array}]$

X = \frac{1}{2} \cdot [\begin{matrix} 2 & 12 4 & 0 \end{matrix}]

$X = \frac{1}{2} \cdot [\begin{array}{c} 2 & 12 \\ 4 & 0 \end{array}]$

Simplify the right side of the equation.

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Multiply

\frac{1}{2}

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

X = [\begin{matrix} \frac{1}{2} \cdot 2 & \frac{1}{2} \cdot 12 \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 0 \end{matrix}]

$X = [\begin{array}{c} \frac{1}{2} \cdot 2 & \frac{1}{2} \cdot 12 \\ \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 0 \end{array}]$

Simplify each element in the matrix.

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Rearrange

\frac{1}{2} \cdot 2

$\frac{1}{2} \cdot 2$ .

X = [\begin{matrix} 1 & \frac{1}{2} \cdot 12 \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 0 \end{matrix}]

$X = [\begin{array}{c} 1 & \frac{1}{2} \cdot 12 \\ \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 0 \end{array}]$

Rearrange

\frac{1}{2} \cdot 12

$\frac{1}{2} \cdot 12$ .

X = [\begin{matrix} 1 & 6 \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 0 \end{matrix}]

$X = [\begin{array}{c} 1 & 6 \\ \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 0 \end{array}]$

Rearrange

\frac{1}{2} \cdot 4

$\frac{1}{2} \cdot 4$ .

X = [\begin{matrix} 1 & 6 2 & \frac{1}{2} \cdot 0 \end{matrix}]

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

Rearrange

\frac{1}{2} \cdot 0

$\frac{1}{2} \cdot 0$ .

X = [\begin{matrix} 1 & 6 2 & 0 \end{matrix}]

$X = [\begin{array}{c} 1 & 6 \\ 2 & 0 \end{array}]$

X = [\begin{matrix} 1 & 6 2 & 0 \end{matrix}]

$X = [\begin{array}{c} 1 & 6 \\ 2 & 0 \end{array}]$

X = [\begin{matrix} 1 & 6 2 & 0 \end{matrix}]

$X = [\begin{array}{c} 1 & 6 \\ 2 & 0 \end{array}]$

X = [\begin{matrix} 1 & 6 2 & 0 \end{matrix}]

$X = [\begin{array}{c} 1 & 6 \\ 2 & 0 \end{array}]$