Algebra Examples

$[\begin{array}{c} 1 & 2 \\ 2 & 1 \\ - 3 & 4 \end{array}] + x = [\begin{array}{c} 5 & - 6 \\ 1 & 0 \\ 8 & 5 \end{array}]$

Step 1

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

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Step 1.1

Subtract $[\begin{array}{c} 1 & 2 \\ 2 & 1 \\ - 3 & 4 \end{array}]$ from both sides of the equation.

$x = [\begin{array}{c} 5 & - 6 \\ 1 & 0 \\ 8 & 5 \end{array}] - [\begin{array}{c} 1 & 2 \\ 2 & 1 \\ - 3 & 4 \end{array}]$

Step 2

Simplify the right side.

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Step 2.1

Subtract the corresponding elements.

$x = [\begin{array}{c} 5 - 1 & - 6 - 2 \\ 1 - 2 & 0 - 1 \\ 8 + 3 & 5 - 4 \end{array}]$

Step 2.2

Simplify each element.

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Step 2.2.1

Subtract $1$ from $5$ .

$x = [\begin{array}{c} 4 & - 6 - 2 \\ 1 - 2 & 0 - 1 \\ 8 + 3 & 5 - 4 \end{array}]$

Step 2.2.2

Subtract $2$ from $- 6$ .

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

Step 2.2.3

Subtract $2$ from $1$ .

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

Step 2.2.4

Subtract $1$ from $0$ .

$x = [\begin{array}{c} 4 & - 8 \\ - 1 & - 1 \\ 8 + 3 & 5 - 4 \end{array}]$

Step 2.2.5

Add $8$ and $3$ .

$x = [\begin{array}{c} 4 & - 8 \\ - 1 & - 1 \\ 11 & 5 - 4 \end{array}]$

Step 2.2.6

Subtract $4$ from $5$ .

$x = [\begin{array}{c} 4 & - 8 \\ - 1 & - 1 \\ 11 & 1 \end{array}]$