Finite Math Examples

$\frac{62.9298 \cdot 0.6909 + 0.3091 x}{100} = 63.546$

Step 1

Multiply both sides by $100$ .

$\frac{62.9298 \cdot 0.6909 + 0.3091 x}{100} \cdot 100 = 63.546 \cdot 100$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{62.9298 \cdot 0.6909 + 0.3091 x}{100} \cdot 100$ .

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Step 2.1.1.1

Simplify the numerator.

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Step 2.1.1.1.1

Factor $0.00000001$ out of $62.9298 \cdot 0.6909 + 0.3091 x$ .

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Step 2.1.1.1.1.1

Factor $0.00000001$ out of $62.9298 \cdot 0.6909$ .

$\frac{0.00000001 (6292980000 \cdot 0.6909) + 0.3091 x}{100} \cdot 100 = 63.546 \cdot 100$

Step 2.1.1.1.1.2

Factor $0.00000001$ out of $0.3091 x$ .

$\frac{0.00000001 (6292980000 \cdot 0.6909) + 0.00000001 (30910000 x)}{100} \cdot 100 = 63.546 \cdot 100$

Step 2.1.1.1.1.3

Factor $0.00000001$ out of $0.00000001 (6292980000 \cdot 0.6909) + 0.00000001 (30910000 x)$ .

$\frac{0.00000001 (6292980000 \cdot 0.6909 + 30910000 x)}{100} \cdot 100 = 63.546 \cdot 100$

Step 2.1.1.1.2

Multiply $6292980000$ by $0.6909$ .

$\frac{0.00000001 (4347819882 + 30910000 x)}{100} \cdot 100 = 63.546 \cdot 100$

Step 2.1.1.1.3

Factor $2$ out of $4347819882 + 30910000 x$ .

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Step 2.1.1.1.3.1

Factor $2$ out of $4347819882$ .

$\frac{0.00000001 (2 (2173909941) + 30910000 x)}{100} \cdot 100 = 63.546 \cdot 100$

Step 2.1.1.1.3.2

Factor $2$ out of $30910000 x$ .

$\frac{0.00000001 (2 (2173909941) + 2 (15455000 x))}{100} \cdot 100 = 63.546 \cdot 100$

Step 2.1.1.1.3.3

Factor $2$ out of $2 (2173909941) + 2 (15455000 x)$ .

$\frac{0.00000001 (2 (2173909941 + 15455000 x))}{100} \cdot 100 = 63.546 \cdot 100$

$\frac{0.00000001 \cdot 2 (2173909941 + 15455000 x)}{100} \cdot 100 = 63.546 \cdot 100$

Step 2.1.1.1.4

Multiply $0.00000001$ by $2$ .

$\frac{0.00000002 (2173909941 + 15455000 x)}{100} \cdot 100 = 63.546 \cdot 100$

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

Cancel the common factor of $0.00000002$ .

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Step 2.1.1.2.1.1

Cancel the common factor.

$\frac{0.00000002 (2173909941 + 15455000 x)}{100} \cdot 100 = 63.546 \cdot 100$

Step 2.1.1.2.1.2

Rewrite the expression.

$\frac{2173909941 + 15455000 x}{100} \cdot \frac{100}{50000000} = 63.546 \cdot 100$

Step 2.1.1.2.2

Simplify terms.

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Step 2.1.1.2.2.1

Cancel the common factor of $100$ .

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Step 2.1.1.2.2.1.1

Cancel the common factor.

$\frac{2173909941 + 15455000 x}{100} \cdot \frac{100}{50000000} = 63.546 \cdot 100$

Step 2.1.1.2.2.1.2

Rewrite the expression.

$(2173909941 + 15455000 x) \cdot \frac{1}{50000000} = 63.546 \cdot 100$

Step 2.1.1.2.2.2

Apply the distributive property.

$2173909941 (\frac{1}{50000000}) + 15455000 x \frac{1}{50000000} = 63.546 \cdot 100$

Step 2.1.1.2.2.3

Combine $2173909941$ and $\frac{1}{50000000}$ .

$\frac{2173909941}{50000000} + 15455000 x \frac{1}{50000000} = 63.546 \cdot 100$

Step 2.1.1.2.2.4

Cancel the common factor of $5000$ .

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Step 2.1.1.2.2.4.1

Factor $5000$ out of $15455000 x$ .

$\frac{2173909941}{50000000} + 5000 (3091 x) \frac{1}{50000000} = 63.546 \cdot 100$

Step 2.1.1.2.2.4.2

Factor $5000$ out of $50000000$ .

$\frac{2173909941}{50000000} + 5000 (3091 x) \frac{1}{5000 (10000)} = 63.546 \cdot 100$

Step 2.1.1.2.2.4.3

Cancel the common factor.

$\frac{2173909941}{50000000} + 5000 (3091 x) \frac{1}{5000 \cdot 10000} = 63.546 \cdot 100$

Step 2.1.1.2.2.4.4

Rewrite the expression.

$\frac{2173909941}{50000000} + 3091 x \frac{1}{10000} = 63.546 \cdot 100$

Step 2.1.1.2.2.5

Combine $3091$ and $\frac{1}{10000}$ .

$\frac{2173909941}{50000000} + x \frac{3091}{10000} = 63.546 \cdot 100$

Step 2.1.1.2.2.6

Combine $x$ and $\frac{3091}{10000}$ .

$\frac{2173909941}{50000000} + \frac{x \cdot 3091}{10000} = 63.546 \cdot 100$

Step 2.1.1.2.3

Move $3091$ to the left of $x$ .

$\frac{2173909941}{50000000} + \frac{3091 x}{10000} = 63.546 \cdot 100$

Step 2.1.1.2.4

Reorder $\frac{2173909941}{50000000}$ and $\frac{3091 x}{10000}$ .

$\frac{3091 x}{10000} + \frac{2173909941}{50000000} = 63.546 \cdot 100$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $63.546$ by $100$ .

$\frac{3091 x}{10000} + \frac{2173909941}{50000000} = 6354.6$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1.1

Subtract $\frac{2173909941}{50000000}$ from both sides of the equation.

$\frac{3091 x}{10000} = 6354.6 - \frac{2173909941}{50000000}$

Step 3.1.2

To write $6354.6$ as a fraction with a common denominator, multiply by $\frac{50000000}{50000000}$ .

$\frac{3091 x}{10000} = 6354.6 \cdot \frac{50000000}{50000000} - \frac{2173909941}{50000000}$

Step 3.1.3

Combine $6354.6$ and $\frac{50000000}{50000000}$ .

$\frac{3091 x}{10000} = \frac{6354.6 \cdot 50000000}{50000000} - \frac{2173909941}{50000000}$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{3091 x}{10000} = \frac{6354.6 \cdot 50000000 - 2173909941}{50000000}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $6354.6$ by $50000000$ .

$\frac{3091 x}{10000} = \frac{317730000000 - 2173909941}{50000000}$

Step 3.1.5.2

Subtract $2173909941$ from $317730000000$ .

$\frac{3091 x}{10000} = \frac{315556090059}{50000000}$

Step 3.1.6

Cancel the common factor of $315556090059$ and $50000000$ .

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Step 3.1.6.1

Rewrite $315556090059$ as $1 (315556090059)$ .

$\frac{3091 x}{10000} = \frac{1 (315556090059)}{50000000}$

Step 3.1.6.2

Cancel the common factors.

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Step 3.1.6.2.1

Rewrite $50000000$ as $1 (50000000)$ .

$\frac{3091 x}{10000} = \frac{1 \cdot 315556090059}{1 \cdot 50000000}$

Step 3.1.6.2.2

Cancel the common factor.

$\frac{3091 x}{10000} = \frac{1 \cdot 315556090059}{1 \cdot 50000000}$

Step 3.1.6.2.3

Rewrite the expression.

$\frac{3091 x}{10000} = \frac{315556090059}{50000000}$

Step 3.2

Multiply both sides of the equation by $\frac{10000}{3091}$ .

$\frac{10000}{3091} \cdot \frac{3091 x}{10000} = \frac{10000}{3091} \cdot \frac{315556090059}{50000000}$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{10000}{3091} \cdot \frac{3091 x}{10000}$ .

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Step 3.3.1.1.1

Cancel the common factor of $10000$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{10000}{3091} \cdot \frac{3091 x}{10000} = \frac{10000}{3091} \cdot \frac{315556090059}{50000000}$

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{3091} (3091 x) = \frac{10000}{3091} \cdot \frac{315556090059}{50000000}$

Step 3.3.1.1.2

Cancel the common factor of $3091$ .

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Step 3.3.1.1.2.1

Factor $3091$ out of $3091 x$ .

$\frac{1}{3091} (3091 (x)) = \frac{10000}{3091} \cdot \frac{315556090059}{50000000}$

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{3091} (3091 x) = \frac{10000}{3091} \cdot \frac{315556090059}{50000000}$

Step 3.3.1.1.2.3

Rewrite the expression.

$x = \frac{10000}{3091} \cdot \frac{315556090059}{50000000}$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Simplify $\frac{10000}{3091} \cdot \frac{315556090059}{50000000}$ .

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Step 3.3.2.1.1

Cancel the common factor of $10000$ .

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Step 3.3.2.1.1.1

Factor $10000$ out of $50000000$ .

$x = \frac{10000}{3091} \cdot \frac{315556090059}{10000 (5000)}$

Step 3.3.2.1.1.2

Cancel the common factor.

$x = \frac{10000}{3091} \cdot \frac{315556090059}{10000 \cdot 5000}$

Step 3.3.2.1.1.3

Rewrite the expression.

$x = \frac{1}{3091} \cdot \frac{315556090059}{5000}$

Step 3.3.2.1.2

Multiply $\frac{1}{3091}$ by $\frac{315556090059}{5000}$ .

$x = \frac{315556090059}{3091 \cdot 5000}$

Step 3.3.2.1.3

Multiply $3091$ by $5000$ .

$x = \frac{315556090059}{15455000}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{315556090059}{15455000}$

Decimal Form:

$x = 20417.73471750 \dots$

Mixed Number Form:

$x = 20417 \frac{11355059}{15455000}$