Finite Math Examples

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} 2 & 1 \\ 4 & 8 \end{array}] - [\begin{array}{c} 3 & 5 \\ 1 & 0 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} 2 - 3 & 1 - 5 \\ 4 - 1 & 8 - 0 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $3$ from $2$ .

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & 1 - 5 \\ 4 - 1 & 8 - 0 \end{array}]$

Step 2.2

Subtract $5$ from $1$ .

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 4 - 1 & 8 - 0 \end{array}]$

Step 2.3

Subtract $1$ from $4$ .

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 - 0 \end{array}]$

Step 2.4

Subtract $0$ from $8$ .

$[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}] - x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}]$

Step 3

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

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Step 3.1

Subtract $[\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}]$ from both sides of the equation.

$- x = [\begin{array}{c} - 1 & - 4 \\ 3 & 8 \end{array}] - [\begin{array}{c} 1 & 10 \\ 7 & 6 \end{array}]$

Step 4

Simplify the right side.

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Step 4.1

Subtract the corresponding elements.

$- x = [\begin{array}{c} - 1 - 1 & - 4 - 10 \\ 3 - 7 & 8 - 6 \end{array}]$

Step 4.2

Simplify each element.

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Step 4.2.1

Subtract $1$ from $- 1$ .

$- x = [\begin{array}{c} - 2 & - 4 - 10 \\ 3 - 7 & 8 - 6 \end{array}]$

Step 4.2.2

Subtract $10$ from $- 4$ .

$- x = [\begin{array}{c} - 2 & - 14 \\ 3 - 7 & 8 - 6 \end{array}]$

Step 4.2.3

Subtract $7$ from $3$ .

$- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 8 - 6 \end{array}]$

Step 4.2.4

Subtract $6$ from $8$ .

$- x = [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

Step 5

Multiply both sides by $- 1$ .

$- - x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

Step 6

Simplify.

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Step 6.1

Multiply $- - x$ .

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Step 6.1.1

Multiply $- 1$ by $- 1$ .

$1 x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

Step 6.1.2

Multiply $x$ by $1$ .

$x = - [\begin{array}{c} - 2 & - 14 \\ - 4 & 2 \end{array}]$

Step 6.2

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

$x = [\begin{array}{c} - - 2 & - - 14 \\ - - 4 & - 1 \cdot 2 \end{array}]$

Step 6.3

Simplify each element in the matrix.

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Step 6.3.1

Multiply $- 1$ by $- 2$ .

$x = [\begin{array}{c} 2 & - - 14 \\ - - 4 & - 1 \cdot 2 \end{array}]$

Step 6.3.2

Multiply $- 1$ by $- 14$ .

$x = [\begin{array}{c} 2 & 14 \\ - - 4 & - 1 \cdot 2 \end{array}]$

Step 6.3.3

Multiply $- 1$ by $- 4$ .

$x = [\begin{array}{c} 2 & 14 \\ 4 & - 1 \cdot 2 \end{array}]$

Step 6.3.4

Multiply $- 1$ by $2$ .

$x = [\begin{array}{c} 2 & 14 \\ 4 & - 2 \end{array}]$