Finite Math Examples

$\frac{1}{3} \cdot (x - 2) - 5$

Step 1

Simplify $\frac{1}{3} \cdot (x - 2) - 5$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$y = \frac{1}{3} x + \frac{1}{3} \cdot - 2 - 5$

Step 1.1.2

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

$y = \frac{x}{3} + \frac{1}{3} \cdot - 2 - 5$

Step 1.1.3

Combine $\frac{1}{3}$ and $- 2$ .

$y = \frac{x}{3} + \frac{- 2}{3} - 5$

Step 1.1.4

Move the negative in front of the fraction.

$y = \frac{x}{3} - \frac{2}{3} - 5$

Step 1.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{x}{3} - \frac{2}{3} - 5 \cdot \frac{3}{3}$

Step 1.3

Combine $- 5$ and $\frac{3}{3}$ .

$y = \frac{x}{3} - \frac{2}{3} + \frac{- 5 \cdot 3}{3}$

Step 1.4

Combine the numerators over the common denominator.

$y = \frac{x}{3} + \frac{- 2 - 5 \cdot 3}{3}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 5$ by $3$ .

$y = \frac{x}{3} + \frac{- 2 - 15}{3}$

Step 1.5.2

Subtract $15$ from $- 2$ .

$y = \frac{x}{3} + \frac{- 17}{3}$

Step 1.6

Move the negative in front of the fraction.

$y = \frac{x}{3} - \frac{17}{3}$

Step 2

Simplify $\frac{1}{3} \cdot (x - 2) - 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{1}{3} x + \frac{1}{3} \cdot - 2 - 5 = 0$

Step 2.1.2

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

$\frac{x}{3} + \frac{1}{3} \cdot - 2 - 5 = 0$

Step 2.1.3

Combine $\frac{1}{3}$ and $- 2$ .

$\frac{x}{3} + \frac{- 2}{3} - 5 = 0$

Step 2.1.4

Move the negative in front of the fraction.

$\frac{x}{3} - \frac{2}{3} - 5 = 0$

Step 2.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} - \frac{2}{3} - 5 \cdot \frac{3}{3} = 0$

Step 2.3

Combine $- 5$ and $\frac{3}{3}$ .

$\frac{x}{3} - \frac{2}{3} + \frac{- 5 \cdot 3}{3} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x}{3} + \frac{- 2 - 5 \cdot 3}{3} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 5$ by $3$ .

$\frac{x}{3} + \frac{- 2 - 15}{3} = 0$

Step 2.5.2

Subtract $15$ from $- 2$ .

$\frac{x}{3} + \frac{- 17}{3} = 0$

Step 2.6

Move the negative in front of the fraction.

$\frac{x}{3} - \frac{17}{3} = 0$

Step 3

Add $\frac{17}{3}$ to both sides of the equation.

$\frac{x}{3} = \frac{17}{3}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = 17$

Step 5