Finite Math Examples

$\frac{34000 + 0.03 x}{34000 + x} = 0.04$

Step 1

Factor $0.01$ out of $34000 + 0.03 x$ .

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Step 1.1

Factor $0.01$ out of $34000$ .

$\frac{0.01 (3400000) + 0.03 x}{34000 + x} = 0.04$

Step 1.2

Factor $0.01$ out of $0.03 x$ .

$\frac{0.01 (3400000) + 0.01 (3 x)}{34000 + x} = 0.04$

Step 1.3

Factor $0.01$ out of $0.01 (3400000) + 0.01 (3 x)$ .

$\frac{0.01 (3400000 + 3 x)}{34000 + x} = 0.04$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$34000 + x, 1$

Step 2.2

Remove parentheses.

$34000 + x, 1$

Step 2.3

The LCM of one and any expression is the expression.

$34000 + x$

Step 3

Multiply each term in $\frac{0.01 (3400000 + 3 x)}{34000 + x} = 0.04$ by $34000 + x$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{0.01 (3400000 + 3 x)}{34000 + x} = 0.04$ by $34000 + x$ .

$\frac{0.01 (3400000 + 3 x)}{34000 + x} (34000 + x) = 0.04 (34000 + x)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.01$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.01 (3400000 + 3 x)}{34000 + x} (34000 + x) = 0.04 (34000 + x)$

Step 3.2.1.2

Rewrite the expression.

$\frac{3400000 + 3 x}{34000 + x} \cdot \frac{34000 + x}{100} = 0.04 (34000 + x)$

Step 3.2.2

Cancel the common factor of $34000 + x$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{3400000 + 3 x}{34000 + x} \cdot \frac{34000 + x}{100} = 0.04 (34000 + x)$

Step 3.2.2.2

Rewrite the expression.

$(3400000 + 3 x) \frac{1}{100} = 0.04 (34000 + x)$

Step 3.2.3

Apply the distributive property.

$3400000 (\frac{1}{100}) + 3 x \frac{1}{100} = 0.04 (34000 + x)$

Step 3.2.4

Cancel the common factor of $100$ .

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Step 3.2.4.1

Factor $100$ out of $3400000$ .

$100 (34000) \frac{1}{100} + 3 x \frac{1}{100} = 0.04 (34000 + x)$

Step 3.2.4.2

Cancel the common factor.

$100 \cdot 34000 \frac{1}{100} + 3 x \frac{1}{100} = 0.04 (34000 + x)$

Step 3.2.4.3

Rewrite the expression.

$34000 + 3 x \frac{1}{100} = 0.04 (34000 + x)$

Step 3.2.5

Multiply $3 x \frac{1}{100}$ .

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Step 3.2.5.1

Combine $3$ and $\frac{1}{100}$ .

$34000 + x \frac{3}{100} = 0.04 (34000 + x)$

Step 3.2.5.2

Combine $x$ and $\frac{3}{100}$ .

$34000 + \frac{x \cdot 3}{100} = 0.04 (34000 + x)$

Step 3.2.6

Move $3$ to the left of $x$ .

$34000 + \frac{3 x}{100} = 0.04 (34000 + x)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$34000 + \frac{3 x}{100} = 0.04 \cdot 34000 + 0.04 x$

Step 3.3.2

Multiply $0.04$ by $34000$ .

$34000 + \frac{3 x}{100} = 1360 + 0.04 x$

Step 4

Solve the equation.

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Step 4.1

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

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Step 4.1.1

Subtract $0.04 x$ from both sides of the equation.

$34000 + \frac{3 x}{100} - 0.04 x = 1360$

Step 4.1.2

To write $- 0.04 x$ as a fraction with a common denominator, multiply by $\frac{100}{100}$ .

$34000 + \frac{3 x}{100} - 0.04 x \cdot \frac{100}{100} = 1360$

Step 4.1.3

Combine $- 0.04 x$ and $\frac{100}{100}$ .

$34000 + \frac{3 x}{100} + \frac{- 0.04 x \cdot 100}{100} = 1360$

Step 4.1.4

Combine the numerators over the common denominator.

$34000 + \frac{3 x - 0.04 x \cdot 100}{100} = 1360$

Step 4.1.5

Simplify each term.

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Step 4.1.5.1

Simplify the numerator.

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Step 4.1.5.1.1

Factor $0.04 x$ out of $3 x - 0.04 x \cdot 100$ .

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Step 4.1.5.1.1.1

Move $x$ .

$34000 + \frac{3 x - 0.04 \cdot 100 x}{100} = 1360$

Step 4.1.5.1.1.2

Factor $0.04 x$ out of $3 x$ .

$34000 + \frac{0.04 x (75) - 0.04 \cdot 100 x}{100} = 1360$

Step 4.1.5.1.1.3

Factor $0.04 x$ out of $- 0.04 \cdot 100 x$ .

$34000 + \frac{0.04 x (75) + 0.04 x (- 1 \cdot 100)}{100} = 1360$

Step 4.1.5.1.1.4

Factor $0.04 x$ out of $0.04 x (75) + 0.04 x (- 1 \cdot 100)$ .

$34000 + \frac{0.04 x (75 - 1 \cdot 100)}{100} = 1360$

Step 4.1.5.1.2

Combine exponents.

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Step 4.1.5.1.2.1

Multiply $- 1$ by $100$ .

$34000 + \frac{0.04 x (75 - 100)}{100} = 1360$

Step 4.1.5.1.2.2

Multiply $75 - 100$ by $0.04$ .

$34000 + \frac{- 1 x}{100} = 1360$

Step 4.1.5.2

Cancel the common factor of $- 1$ and $100$ .

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Step 4.1.5.2.1

Factor $1$ out of $- 1 x$ .

$34000 + \frac{1 (- x)}{100} = 1360$

Step 4.1.5.2.2

Cancel the common factors.

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Step 4.1.5.2.2.1

Rewrite $100$ as $1 (100)$ .

$34000 + \frac{1 (- x)}{1 (100)} = 1360$

Step 4.1.5.2.2.2

Cancel the common factor.

$34000 + \frac{1 (- x)}{1 \cdot 100} = 1360$

Step 4.1.5.2.2.3

Rewrite the expression.

$34000 + \frac{- x}{100} = 1360$

Step 4.1.5.3

Move the negative in front of the fraction.

$34000 - \frac{x}{100} = 1360$

Step 4.2

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

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Step 4.2.1

Subtract $34000$ from both sides of the equation.

$- \frac{x}{100} = 1360 - 34000$

Step 4.2.2

Subtract $34000$ from $1360$ .

$- \frac{x}{100} = - 32640$

Step 4.3

Multiply both sides of the equation by $- 100$ .

$- 100 (- \frac{x}{100}) = - 100 \cdot - 32640$

Step 4.4

Simplify both sides of the equation.

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Step 4.4.1

Simplify the left side.

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Step 4.4.1.1

Simplify $- 100 (- \frac{x}{100})$ .

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Step 4.4.1.1.1

Cancel the common factor of $100$ .

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Step 4.4.1.1.1.1

Move the leading negative in $- \frac{x}{100}$ into the numerator.

$- 100 \frac{- x}{100} = - 100 \cdot - 32640$

Step 4.4.1.1.1.2

Factor $100$ out of $- 100$ .

$100 (- 1) \frac{- x}{100} = - 100 \cdot - 32640$

Step 4.4.1.1.1.3

Cancel the common factor.

$100 \cdot - 1 \frac{- x}{100} = - 100 \cdot - 32640$

Step 4.4.1.1.1.4

Rewrite the expression.

$- - x = - 100 \cdot - 32640$

Step 4.4.1.1.2

Multiply.

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Step 4.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 100 \cdot - 32640$

Step 4.4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 100 \cdot - 32640$

Step 4.4.2

Simplify the right side.

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Step 4.4.2.1

Multiply $- 100$ by $- 32640$ .

$x = 3264000$