Finite Math Examples

3 x \cdot 1 + 2 x \cdot 2 + 3 x \cdot 3 = 5

$3 x \cdot 1 + 2 x \cdot 2 + 3 x \cdot 3 = 5$ ,

- 5 x \cdot 1 - 5 x \cdot 2 - 4 x \cdot 3 = - 3

$- 5 x \cdot 1 - 5 x \cdot 2 - 4 x \cdot 3 = - 3$ ,

3 x \cdot 1 - x \cdot 2 - 2 x \cdot 3 = 1

$3 x \cdot 1 - x \cdot 2 - 2 x \cdot 3 = 1$

Step 1

Divide each term in

16 x = 5

$16 x = 5$ by

16

$16$ and simplify.

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Step 1.1

Divide each term in

16 x = 5

$16 x = 5$ by

16

$16$ .

\frac{16 x}{16} = \frac{5}{16}

$\frac{16 x}{16} = \frac{5}{16}$

- 27 x = - 3

$- 27 x = - 3$

- 5 x = 1

$- 5 x = 1$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of

16

$16$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{16 x}{16} = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

Step 1.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

$x = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

$x = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

$x = \frac{5}{16}$

$- 27 x = - 3$

$- 5 x = 1$

Step 2

Replace all occurrences of

$x$ with

$\frac{5}{16}$ in each equation.

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Step 2.1

Replace all occurrences of

$x$ in

$- 27 x = - 3$ with

$\frac{5}{16}$ .

$- 27 (\frac{5}{16}) = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify

$- 27 (\frac{5}{16})$ .

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Step 2.2.1.1

Multiply

$- 27 (\frac{5}{16})$ .

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Step 2.2.1.1.1

Combine

$- 27$ and

$\frac{5}{16}$ .

$\frac{- 27 \cdot 5}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

Step 2.2.1.1.2

Multiply

$- 27$ by

$5$ .

$\frac{- 135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

$\frac{- 135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

Step 2.2.1.2

Move the negative in front of the fraction.

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- 5 x = 1$

Step 2.3

Replace all occurrences of

$x$ in

$- 5 x = 1$ with

$\frac{5}{16}$ .

$- 5 (\frac{5}{16}) = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify

$- 5 (\frac{5}{16})$ .

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Step 2.4.1.1

Multiply

$- 5 (\frac{5}{16})$ .

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Step 2.4.1.1.1

Combine

$- 5$ and

$\frac{5}{16}$ .

$\frac{- 5 \cdot 5}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

Step 2.4.1.1.2

Multiply

$- 5$ by

$5$ .

$\frac{- 25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$\frac{- 25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

Step 2.4.1.2

Move the negative in front of the fraction.

$- \frac{25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- \frac{25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- \frac{25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

$- \frac{25}{16} = 1$

$- \frac{135}{16} = - 3$

$x = \frac{5}{16}$

Step 3

Since

$- \frac{25}{16} = 1$ is not true, there is no solution.

No solution

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$