Finite Math Examples

$x \cdot 1 = 0.0412 (2000000 - x \cdot 2 - x \cdot 3 - x \cdot 4)$ , $x \cdot 2 = 0.0328 (2000000 - x \cdot 1 - x \cdot 3 - x \cdot 4)$ , $x \cdot 3 = 0.0285 (2000000 - x \cdot 1 - x \cdot 2 - x \cdot 4)$ , $x \cdot 4 = 0.0232 (2000000 - x \cdot 1 - x \cdot 2 - x \cdot 3)$

Step 1

Solve for $x$ in $x = 0.0412 (2000000 - 9 x)$ .

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Step 1.1

Simplify $0.0412 (2000000 - 9 x)$ .

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Step 1.1.1

Apply the distributive property.

$x = 0.0412 \cdot 2000000 + 0.0412 (- 9 x)$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 1.1.2

Multiply.

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Step 1.1.2.1

Multiply $0.0412$ by $2000000$ .

$x = 82400 + 0.0412 (- 9 x)$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 1.1.2.2

Multiply $- 9$ by $0.0412$ .

$x = 82400 - 0.3708 x$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$x = 82400 - 0.3708 x$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$x = 82400 - 0.3708 x$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 1.2

Move all terms containing $x$ to the left side of the equation.

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Step 1.2.1

Add $0.3708 x$ to both sides of the equation.

$x + 0.3708 x = 82400$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 1.2.2

Add $x$ and $0.3708 x$ .

$1.3708 x = 82400$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$1.3708 x = 82400$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 1.3

Divide each term in $1.3708 x = 82400$ by $1.3708$ and simplify.

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Step 1.3.1

Divide each term in $1.3708 x = 82400$ by $1.3708$ .

$\frac{1.3708 x}{1.3708} = \frac{82400}{1.3708}$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $1.3708$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{1.3708 x}{1.3708} = \frac{82400}{1.3708}$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{82400}{1.3708}$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$x = \frac{82400}{1.3708}$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$x = \frac{82400}{1.3708}$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $82400$ by $1.3708$ .

$x = 60110.88415523$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$x = 60110.88415523$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$x = 60110.88415523$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$x = 60110.88415523$

$x \cdot 2 = 0.0328 (2000000 - 8 x)$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2

Replace all occurrences of $x$ with $60110.88415523$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x \cdot 2 = 0.0328 (2000000 - 8 x)$ with $60110.88415523$ .

$(60110.88415523) \cdot 2 = 0.0328 (2000000 - 8 \cdot 60110.88415523)$

$x = 60110.88415523$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.2

Simplify $(60110.88415523) \cdot 2 = 0.0328 (2000000 - 8 \cdot 60110.88415523)$ .

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Multiply $60110.88415523$ by $2$ .

$120221.76831047 = 0.0328 (2000000 - 8 \cdot 60110.88415523)$

$x = 60110.88415523$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$120221.76831047 = 0.0328 (2000000 - 8 \cdot 60110.88415523)$

$x = 60110.88415523$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify $0.0328 (2000000 - 8 \cdot 60110.88415523)$ .

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Step 2.2.2.1.1

Multiply $- 8$ by $60110.88415523$ .

$120221.76831047 = 0.0328 (2000000 - 480887.0732419)$

$x = 60110.88415523$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.2.2.1.2

Subtract $480887.0732419$ from $2000000$ .

$120221.76831047 = 0.0328 \cdot 1519112.92675809$

$x = 60110.88415523$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.2.2.1.3

Multiply $0.0328$ by $1519112.92675809$ .

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 3 = 0.0285 (2000000 - 7 x)$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.3

Replace all occurrences of $x$ in $x \cdot 3 = 0.0285 (2000000 - 7 x)$ with $60110.88415523$ .

$(60110.88415523) \cdot 3 = 0.0285 (2000000 - 7 \cdot 60110.88415523)$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.4

Simplify $(60110.88415523) \cdot 3 = 0.0285 (2000000 - 7 \cdot 60110.88415523)$ .

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Multiply $60110.88415523$ by $3$ .

$180332.65246571 = 0.0285 (2000000 - 7 \cdot 60110.88415523)$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$180332.65246571 = 0.0285 (2000000 - 7 \cdot 60110.88415523)$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $0.0285 (2000000 - 7 \cdot 60110.88415523)$ .

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Step 2.4.2.1.1

Multiply $- 7$ by $60110.88415523$ .

$180332.65246571 = 0.0285 (2000000 - 420776.18908666)$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.4.2.1.2

Subtract $420776.18908666$ from $2000000$ .

$180332.65246571 = 0.0285 \cdot 1579223.81091333$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.4.2.1.3

Multiply $0.0285$ by $1579223.81091333$ .

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$x \cdot 4 = 0.0232 (2000000 - 6 x)$

Step 2.5

Replace all occurrences of $x$ in $x \cdot 4 = 0.0232 (2000000 - 6 x)$ with $60110.88415523$ .

$(60110.88415523) \cdot 4 = 0.0232 (2000000 - 6 \cdot 60110.88415523)$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

Step 2.6

Simplify $(60110.88415523) \cdot 4 = 0.0232 (2000000 - 6 \cdot 60110.88415523)$ .

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Step 2.6.1

Simplify the left side.

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Step 2.6.1.1

Multiply $60110.88415523$ by $4$ .

$240443.53662095 = 0.0232 (2000000 - 6 \cdot 60110.88415523)$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$240443.53662095 = 0.0232 (2000000 - 6 \cdot 60110.88415523)$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

Step 2.6.2

Simplify the right side.

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Step 2.6.2.1

Simplify $0.0232 (2000000 - 6 \cdot 60110.88415523)$ .

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Step 2.6.2.1.1

Multiply $- 6$ by $60110.88415523$ .

$240443.53662095 = 0.0232 (2000000 - 360665.30493142)$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

Step 2.6.2.1.2

Subtract $360665.30493142$ from $2000000$ .

$240443.53662095 = 0.0232 \cdot 1639334.69506857$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

Step 2.6.2.1.3

Multiply $0.0232$ by $1639334.69506857$ .

$240443.53662095 = 38032.56492559$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$240443.53662095 = 38032.56492559$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$240443.53662095 = 38032.56492559$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$240443.53662095 = 38032.56492559$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

$240443.53662095 = 38032.56492559$

$180332.65246571 = 45007.87861103$

$120221.76831047 = 49826.90399766$

$x = 60110.88415523$

Step 3

Since $240443.53662095 = 38032.56492559$ is not true, there is no solution.

No solution

Step 4