Finite Math Examples

$0.066 = \frac{25000 - x}{(x) (\frac{10}{12})}$

Step 1

Rewrite the equation as $\frac{25000 - x}{x (\frac{10}{12})} = 0.066$ .

$\frac{25000 - x}{x (\frac{10}{12})} = 0.066$

Step 2

Factor each term.

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Step 2.1

Cancel the common factor of $10$ and $12$ .

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Step 2.1.1

Factor $2$ out of $10$ .

$\frac{25000 - x}{x \frac{2 (5)}{12}} = 0.066$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $12$ .

$\frac{25000 - x}{x \frac{2 \cdot 5}{2 \cdot 6}} = 0.066$

Step 2.1.2.2

Cancel the common factor.

$\frac{25000 - x}{x \frac{2 \cdot 5}{2 \cdot 6}} = 0.066$

Step 2.1.2.3

Rewrite the expression.

$\frac{25000 - x}{x \frac{5}{6}} = 0.066$

Step 2.2

Combine $x$ and $\frac{5}{6}$ .

$\frac{25000 - x}{\frac{x \cdot 5}{6}} = 0.066$

Step 2.3

Simplify the denominator.

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Step 2.3.1

Move $5$ to the left of $x$ .

$\frac{25000 - x}{\frac{5 \cdot x}{6}} = 0.066$

Step 2.3.2

Multiply $5$ by $x$ .

$\frac{25000 - x}{\frac{5 x}{6}} = 0.066$

Step 2.4

Multiply the numerator by the reciprocal of the denominator.

$(25000 - x) \frac{6}{5 x} = 0.066$

Step 2.5

Multiply $25000 - x$ by $\frac{6}{5 x}$ .

$\frac{(25000 - x) \cdot 6}{5 x} = 0.066$

Step 2.6

Move $6$ to the left of $25000 - x$ .

$\frac{6 \cdot (25000 - x)}{5 x} = 0.066$

Step 2.7

Multiply $6$ by $25000 - x$ .

$\frac{6 (25000 - x)}{5 x} = 0.066$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$5 x, 1$

Step 3.2

The LCM of one and any expression is the expression.

$5 x$

Step 4

Multiply each term in $\frac{6 (25000 - x)}{5 x} = 0.066$ by $5 x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{6 (25000 - x)}{5 x} = 0.066$ by $5 x$ .

$\frac{6 (25000 - x)}{5 x} (5 x) = 0.066 (5 x)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Rewrite using the commutative property of multiplication.

$5 \frac{6 (25000 - x)}{5 x} x = 0.066 (5 x)$

Step 4.2.2

Cancel the common factor of $5$ .

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Step 4.2.2.1

Factor $5$ out of $5 x$ .

$5 \frac{6 (25000 - x)}{5 (x)} x = 0.066 (5 x)$

Step 4.2.2.2

Cancel the common factor.

$5 \frac{6 (25000 - x)}{5 x} x = 0.066 (5 x)$

Step 4.2.2.3

Rewrite the expression.

$\frac{6 (25000 - x)}{x} x = 0.066 (5 x)$

Step 4.2.3

Cancel the common factor of $x$ .

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Step 4.2.3.1

Cancel the common factor.

$\frac{6 (25000 - x)}{x} x = 0.066 (5 x)$

Step 4.2.3.2

Rewrite the expression.

$6 (25000 - x) = 0.066 (5 x)$

Step 4.2.4

Apply the distributive property.

$6 \cdot 25000 + 6 (- x) = 0.066 (5 x)$

Step 4.2.5

Multiply.

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Step 4.2.5.1

Multiply $6$ by $25000$ .

$150000 + 6 (- x) = 0.066 (5 x)$

Step 4.2.5.2

Multiply $- 1$ by $6$ .

$150000 - 6 x = 0.066 (5 x)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply $5$ by $0.066$ .

$150000 - 6 x = 0.33 x$

Step 5

Solve the equation.

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Step 5.1

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

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Step 5.1.1

Subtract $0.33 x$ from both sides of the equation.

$150000 - 6 x - 0.33 x = 0$

Step 5.1.2

Subtract $0.33 x$ from $- 6 x$ .

$150000 - 6.33 x = 0$

Step 5.2

Subtract $150000$ from both sides of the equation.

$- 6.33 x = - 150000$

Step 5.3

Divide each term in $- 6.33 x = - 150000$ by $- 6.33$ and simplify.

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Step 5.3.1

Divide each term in $- 6.33 x = - 150000$ by $- 6.33$ .

$\frac{- 6.33 x}{- 6.33} = \frac{- 150000}{- 6.33}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $- 6.33$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{- 6.33 x}{- 6.33} = \frac{- 150000}{- 6.33}$

Step 5.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 150000}{- 6.33}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Divide $- 150000$ by $- 6.33$ .

$x = 23696.68246445$