Finite Math Examples

$- \frac{1}{2} + \frac{1}{5} x - (\frac{2}{5} x - 27 (5 x - \frac{5}{2}))$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{5}$ and $x$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{2}{5} x - 27 (5 x - \frac{5}{2}))$

Step 1.2

Simplify each term.

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Step 1.2.1

Combine $\frac{2}{5}$ and $x$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{2 x}{5} - 27 (5 x - \frac{5}{2}))$

Step 1.2.2

Apply the distributive property.

$- \frac{1}{2} + \frac{x}{5} - (\frac{2 x}{5} - 27 (5 x) - 27 (- \frac{5}{2}))$

Step 1.2.3

Multiply $5$ by $- 27$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{2 x}{5} - 135 x - 27 (- \frac{5}{2}))$

Step 1.2.4

Multiply $- 27 (- \frac{5}{2})$ .

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Step 1.2.4.1

Multiply $- 1$ by $- 27$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{2 x}{5} - 135 x + 27 (\frac{5}{2}))$

Step 1.2.4.2

Combine $27$ and $\frac{5}{2}$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{2 x}{5} - 135 x + \frac{27 \cdot 5}{2})$

Step 1.2.4.3

Multiply $27$ by $5$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{2 x}{5} - 135 x + \frac{135}{2})$

Step 1.3

To write $- 135 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{2 x}{5} - 135 x \cdot \frac{5}{5} + \frac{135}{2})$

Step 1.4

Combine $- 135 x$ and $\frac{5}{5}$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{2 x}{5} + \frac{- 135 x \cdot 5}{5} + \frac{135}{2})$

Step 1.5

Combine the numerators over the common denominator.

$- \frac{1}{2} + \frac{x}{5} - (\frac{2 x - 135 x \cdot 5}{5} + \frac{135}{2})$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $x$ out of $2 x - 135 x \cdot 5$ .

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Step 1.6.1.1.1

Factor $x$ out of $2 x$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{x \cdot 2 - 135 x \cdot 5}{5} + \frac{135}{2})$

Step 1.6.1.1.2

Factor $x$ out of $- 135 x \cdot 5$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{x \cdot 2 + x (- 135 \cdot 5)}{5} + \frac{135}{2})$

Step 1.6.1.1.3

Factor $x$ out of $x \cdot 2 + x (- 135 \cdot 5)$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{x (2 - 135 \cdot 5)}{5} + \frac{135}{2})$

Step 1.6.1.2

Multiply $- 135$ by $5$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{x (2 - 675)}{5} + \frac{135}{2})$

Step 1.6.1.3

Subtract $675$ from $2$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{x \cdot - 673}{5} + \frac{135}{2})$

Step 1.6.2

Move $- 673$ to the left of $x$ .

$- \frac{1}{2} + \frac{x}{5} - (\frac{- 673 \cdot x}{5} + \frac{135}{2})$

Step 1.6.3

Move the negative in front of the fraction.

$- \frac{1}{2} + \frac{x}{5} - (- \frac{673 x}{5} + \frac{135}{2})$

Step 1.7

Apply the distributive property.

$- \frac{1}{2} + \frac{x}{5} - - \frac{673 x}{5} - \frac{135}{2}$

Step 1.8

Multiply $- - \frac{673 x}{5}$ .

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Step 1.8.1

Multiply $- 1$ by $- 1$ .

$- \frac{1}{2} + \frac{x}{5} + 1 \frac{673 x}{5} - \frac{135}{2}$

Step 1.8.2

Multiply $\frac{673 x}{5}$ by $1$ .

$- \frac{1}{2} + \frac{x}{5} + \frac{673 x}{5} - \frac{135}{2}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{- 1 - 135}{2} + \frac{x + 673 x}{5}$

Step 2.2

Subtract $135$ from $- 1$ .

$\frac{- 136}{2} + \frac{x + 673 x}{5}$

Step 2.3

Add $x$ and $673 x$ .

$\frac{- 136}{2} + \frac{674 x}{5}$

Step 2.4

Divide $- 136$ by $2$ .

$- 68 + \frac{674 x}{5}$