Finite Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $- 3$ by each element of the matrix.

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

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $- 3$ by $2$ .

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

Step 1.2.2

Multiply $- 3$ by $- 8$ .

$x + [\begin{array}{c} - 6 & 24 \\ - 3 \cdot - 4 & - 3 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.3

Multiply $- 3$ by $- 4$ .

$x + [\begin{array}{c} - 6 & 24 \\ 12 & - 3 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.4

Multiply $- 3$ by $2$ .

$x + [\begin{array}{c} - 6 & 24 \\ 12 & - 6 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2

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

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Step 2.1

Subtract $[\begin{array}{c} - 6 & 24 \\ 12 & - 6 \end{array}]$ from both sides of the equation.

$x = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} - 6 & 24 \\ 12 & - 6 \end{array}]$

Step 3

Simplify the right side.

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Step 3.1

Subtract the corresponding elements.

$x = [\begin{array}{c} 4 + 6 & - 6 - 24 \\ 2 - 12 & - 8 + 6 \end{array}]$

Step 3.2

Simplify each element.

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Step 3.2.1

Add $4$ and $6$ .

$x = [\begin{array}{c} 10 & - 6 - 24 \\ 2 - 12 & - 8 + 6 \end{array}]$

Step 3.2.2

Subtract $24$ from $- 6$ .

$x = [\begin{array}{c} 10 & - 30 \\ 2 - 12 & - 8 + 6 \end{array}]$

Step 3.2.3

Subtract $12$ from $2$ .

$x = [\begin{array}{c} 10 & - 30 \\ - 10 & - 8 + 6 \end{array}]$

Step 3.2.4

Add $- 8$ and $6$ .

$x = [\begin{array}{c} 10 & - 30 \\ - 10 & - 2 \end{array}]$