Finite Math Examples

$\frac{x}{5} + \frac{3}{25} \cdot (12000 - x)$

Step 1

Simplify $\frac{x}{5} + \frac{3}{25} \cdot (12000 - x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$y = \frac{x}{5} + \frac{3}{25} \cdot 12000 + \frac{3}{25} (- x)$

Step 1.1.2

Cancel the common factor of $25$ .

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Step 1.1.2.1

Factor $25$ out of $12000$ .

$y = \frac{x}{5} + \frac{3}{25} \cdot (25 (480)) + \frac{3}{25} (- x)$

Step 1.1.2.2

Cancel the common factor.

$y = \frac{x}{5} + \frac{3}{25} \cdot (25 \cdot 480) + \frac{3}{25} (- x)$

Step 1.1.2.3

Rewrite the expression.

$y = \frac{x}{5} + 3 \cdot 480 + \frac{3}{25} (- x)$

Step 1.1.3

Multiply $3$ by $480$ .

$y = \frac{x}{5} + 1440 + \frac{3}{25} (- x)$

Step 1.1.4

Combine $\frac{3}{25}$ and $x$ .

$y = \frac{x}{5} + 1440 - \frac{3 x}{25}$

Step 1.2

To write $\frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{x}{5} \cdot \frac{5}{5} - \frac{3 x}{25} + 1440$

Step 1.3

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{5}$ by $\frac{5}{5}$ .

$y = \frac{x \cdot 5}{5 \cdot 5} - \frac{3 x}{25} + 1440$

Step 1.3.2

Multiply $5$ by $5$ .

$y = \frac{x \cdot 5}{25} - \frac{3 x}{25} + 1440$

Step 1.4

Combine the numerators over the common denominator.

$y = \frac{x \cdot 5 - 3 x}{25} + 1440$

Step 1.5

Subtract $3 x$ from $x \cdot 5$ .

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Step 1.5.1

Reorder $x$ and $5$ .

$y = \frac{5 \cdot x - 3 x}{25} + 1440$

Step 1.5.2

Subtract $3 x$ from $5 \cdot x$ .

$y = \frac{2 \cdot x}{25} + 1440$

$y = \frac{2 x}{25} + 1440$

Step 2

Simplify $\frac{x}{5} + \frac{3}{25} \cdot (12000 - x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{x}{5} + \frac{3}{25} \cdot 12000 + \frac{3}{25} (- x) = 0$

Step 2.1.2

Cancel the common factor of $25$ .

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Step 2.1.2.1

Factor $25$ out of $12000$ .

$\frac{x}{5} + \frac{3}{25} \cdot (25 (480)) + \frac{3}{25} (- x) = 0$

Step 2.1.2.2

Cancel the common factor.

$\frac{x}{5} + \frac{3}{25} \cdot (25 \cdot 480) + \frac{3}{25} (- x) = 0$

Step 2.1.2.3

Rewrite the expression.

$\frac{x}{5} + 3 \cdot 480 + \frac{3}{25} (- x) = 0$

Step 2.1.3

Multiply $3$ by $480$ .

$\frac{x}{5} + 1440 + \frac{3}{25} (- x) = 0$

Step 2.1.4

Combine $\frac{3}{25}$ and $x$ .

$\frac{x}{5} + 1440 - \frac{3 x}{25} = 0$

Step 2.2

To write $\frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{5} \cdot \frac{5}{5} - \frac{3 x}{25} + 1440 = 0$

Step 2.3

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{x}{5}$ by $\frac{5}{5}$ .

$\frac{x \cdot 5}{5 \cdot 5} - \frac{3 x}{25} + 1440 = 0$

Step 2.3.2

Multiply $5$ by $5$ .

$\frac{x \cdot 5}{25} - \frac{3 x}{25} + 1440 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - 3 x}{25} + 1440 = 0$

Step 2.5

Subtract $3 x$ from $x \cdot 5$ .

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Step 2.5.1

Reorder $x$ and $5$ .

$\frac{5 \cdot x - 3 x}{25} + 1440 = 0$

Step 2.5.2

Subtract $3 x$ from $5 \cdot x$ .

$\frac{2 \cdot x}{25} + 1440 = 0$

$\frac{2 x}{25} + 1440 = 0$

Step 3

Subtract $1440$ from both sides of the equation.

$\frac{2 x}{25} = - 1440$

Step 4

Multiply both sides of the equation by $\frac{25}{2}$ .

$\frac{25}{2} \cdot \frac{2 x}{25} = \frac{25}{2} \cdot - 1440$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{25}{2} \cdot \frac{2 x}{25}$ .

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Step 5.1.1.1

Cancel the common factor of $25$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{25}{2} \cdot \frac{2 x}{25} = \frac{25}{2} \cdot - 1440$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{25}{2} \cdot - 1440$

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{25}{2} \cdot - 1440$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{25}{2} \cdot - 1440$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{25}{2} \cdot - 1440$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{25}{2} \cdot - 1440$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Factor $2$ out of $- 1440$ .

$x = \frac{25}{2} \cdot (2 (- 720))$

Step 5.2.1.1.2

Cancel the common factor.

$x = \frac{25}{2} \cdot (2 \cdot - 720)$

Step 5.2.1.1.3

Rewrite the expression.

$x = 25 \cdot - 720$

Step 5.2.1.2

Multiply $25$ by $- 720$ .

$x = - 18000$

Step 6