Finite Math Examples

- 2 x [\begin{matrix} 2 & - 8 - 4 & 2 \end{matrix}] = [\begin{matrix} 4 & - 6 2 & - 8 \end{matrix}]

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

Step 1

Multiply

- 2 x

$- 2 x$ by each element of the matrix.

[\begin{matrix} - 2 x \cdot 2 & - 2 x \cdot - 8 - 2 x \cdot - 4 & - 2 x \cdot 2 \end{matrix}] = [\begin{matrix} 4 & - 6 2 & - 8 \end{matrix}]

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

Step 2

Simplify each element in the matrix.

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Step 2.1

Multiply

2

$2$ by

- 2

$- 2$ .

[\begin{matrix} - 4 x & - 2 x \cdot - 8 - 2 x \cdot - 4 & - 2 x \cdot 2 \end{matrix}] = [\begin{matrix} 4 & - 6 2 & - 8 \end{matrix}]

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

Step 2.2

Multiply

- 8

$- 8$ by

- 2

$- 2$ .

[\begin{matrix} - 4 x & 16 x - 2 x \cdot - 4 & - 2 x \cdot 2 \end{matrix}] = [\begin{matrix} 4 & - 6 2 & - 8 \end{matrix}]

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

Step 2.3

Multiply

- 4

$- 4$ by

- 2

$- 2$ .

[\begin{matrix} - 4 x & 16 x 8 x & - 2 x \cdot 2 \end{matrix}] = [\begin{matrix} 4 & - 6 2 & - 8 \end{matrix}]

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

Step 2.4

Multiply

2

$2$ by

- 2

$- 2$ .

[\begin{matrix} - 4 x & 16 x 8 x & - 4 x \end{matrix}] = [\begin{matrix} 4 & - 6 2 & - 8 \end{matrix}]

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

[\begin{matrix} - 4 x & 16 x 8 x & - 4 x \end{matrix}] = [\begin{matrix} 4 & - 6 2 & - 8 \end{matrix}]

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

Step 3

Write as a linear system of equations.

- 4 x = 4

$- 4 x = 4$

16 x = - 6

$16 x = - 6$

8 x = 2

$8 x = 2$

- 4 x = - 8

$- 4 x = - 8$

Step 4

Solve the system of equations.

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Step 4.1

Divide each term in

- 4 x = 4

$- 4 x = 4$ by

- 4

$- 4$ and simplify.

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Step 4.1.1

Divide each term in

- 4 x = 4

$- 4 x = 4$ by

- 4

$- 4$ .

\frac{- 4 x}{- 4} = \frac{4}{- 4}

$\frac{- 4 x}{- 4} = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of

$- 4$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

Step 4.1.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

$x = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

$x = \frac{4}{- 4}$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

Step 4.1.3

Simplify the right side.

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Step 4.1.3.1

Divide

$4$ by

$- 4$ .

$x = - 1$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

$x = - 1$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

$x = - 1$

$16 x = - 6$

$8 x = 2$

$- 4 x = - 8$

Step 4.2

Replace all occurrences of

$x$ with

$- 1$ in each equation.

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Step 4.2.1

Replace all occurrences of

$x$ in

$16 x = - 6$ with

$- 1$ .

$16 (- 1) = - 6$

$x = - 1$

$8 x = 2$

$- 4 x = - 8$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Multiply

$16$ by

$- 1$ .

$- 16 = - 6$

$x = - 1$

$8 x = 2$

$- 4 x = - 8$

$- 16 = - 6$

$x = - 1$

$8 x = 2$

$- 4 x = - 8$

Step 4.2.3

Replace all occurrences of

$x$ in

$8 x = 2$ with

$- 1$ .

$8 (- 1) = 2$

$- 16 = - 6$

$x = - 1$

$- 4 x = - 8$

Step 4.2.4

Simplify the left side.

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Step 4.2.4.1

Multiply

$8$ by

$- 1$ .

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

$- 4 x = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

$- 4 x = - 8$

Step 4.2.5

Replace all occurrences of

$x$ in

$- 4 x = - 8$ with

$- 1$ .

$- 4 \cdot - 1 = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

Step 4.2.6

Simplify the left side.

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Step 4.2.6.1

Multiply

$- 4$ by

$- 1$ .

$4 = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

$4 = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

$4 = - 8$

$- 8 = 2$

$- 16 = - 6$

$x = - 1$

Step 4.3

Since

$4 = - 8$ is not true, there is no solution.

$No solution$