Finite Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply $4$ by each element of the matrix.

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

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $4$ by $2$ .

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

Step 1.2.2

Multiply $4$ by $- 8$ .

$- x + [\begin{array}{c} 8 & - 32 \\ 4 \cdot - 4 & 4 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.3

Multiply $4$ by $- 4$ .

$- x + [\begin{array}{c} 8 & - 32 \\ - 16 & 4 \cdot 2 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 1.2.4

Multiply $4$ by $2$ .

$- x + [\begin{array}{c} 8 & - 32 \\ - 16 & 8 \end{array}] = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}]$

Step 2

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

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Step 2.1

Subtract $[\begin{array}{c} 8 & - 32 \\ - 16 & 8 \end{array}]$ from both sides of the equation.

$- x = [\begin{array}{c} 4 & - 6 \\ 2 & - 8 \end{array}] - [\begin{array}{c} 8 & - 32 \\ - 16 & 8 \end{array}]$

Step 3

Simplify the right side.

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Step 3.1

Subtract the corresponding elements.

$- x = [\begin{array}{c} 4 - 8 & - 6 + 32 \\ 2 + 16 & - 8 - 8 \end{array}]$

Step 3.2

Simplify each element.

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Step 3.2.1

Subtract $8$ from $4$ .

$- x = [\begin{array}{c} - 4 & - 6 + 32 \\ 2 + 16 & - 8 - 8 \end{array}]$

Step 3.2.2

Add $- 6$ and $32$ .

$- x = [\begin{array}{c} - 4 & 26 \\ 2 + 16 & - 8 - 8 \end{array}]$

Step 3.2.3

Add $2$ and $16$ .

$- x = [\begin{array}{c} - 4 & 26 \\ 18 & - 8 - 8 \end{array}]$

Step 3.2.4

Subtract $8$ from $- 8$ .

$- x = [\begin{array}{c} - 4 & 26 \\ 18 & - 16 \end{array}]$

Step 4

Multiply both sides by $- 1$ .

$- - x = - [\begin{array}{c} - 4 & 26 \\ 18 & - 16 \end{array}]$

Step 5

Simplify.

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Step 5.1

Multiply $- - x$ .

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Step 5.1.1

Multiply $- 1$ by $- 1$ .

$1 x = - [\begin{array}{c} - 4 & 26 \\ 18 & - 16 \end{array}]$

Step 5.1.2

Multiply $x$ by $1$ .

$x = - [\begin{array}{c} - 4 & 26 \\ 18 & - 16 \end{array}]$

Step 5.2

Multiply $- 1$ by each element of the matrix.

$x = [\begin{array}{c} - - 4 & - 1 \cdot 26 \\ - 1 \cdot 18 & - - 16 \end{array}]$

Step 5.3

Simplify each element in the matrix.

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Step 5.3.1

Multiply $- 1$ by $- 4$ .

$x = [\begin{array}{c} 4 & - 1 \cdot 26 \\ - 1 \cdot 18 & - - 16 \end{array}]$

Step 5.3.2

Multiply $- 1$ by $26$ .

$x = [\begin{array}{c} 4 & - 26 \\ - 1 \cdot 18 & - - 16 \end{array}]$

Step 5.3.3

Multiply $- 1$ by $18$ .

$x = [\begin{array}{c} 4 & - 26 \\ - 18 & - - 16 \end{array}]$

Step 5.3.4

Multiply $- 1$ by $- 16$ .

$x = [\begin{array}{c} 4 & - 26 \\ - 18 & 16 \end{array}]$