Finite Math Examples

$15 - \frac{1}{15} x = \frac{1}{10} x$

Step 1

Combine $x$ and $\frac{1}{15}$ .

$15 - \frac{x}{15} = \frac{1}{10} x$

Step 2

Combine $\frac{1}{10}$ and $x$ .

$15 - \frac{x}{15} = \frac{x}{10}$

Step 3

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

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Step 3.1

Subtract $\frac{x}{10}$ from both sides of the equation.

$15 - \frac{x}{15} - \frac{x}{10} = 0$

Step 3.2

To write $- \frac{x}{15}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$15 - \frac{x}{15} \cdot \frac{2}{2} - \frac{x}{10} = 0$

Step 3.3

To write $- \frac{x}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$15 - \frac{x}{15} \cdot \frac{2}{2} - \frac{x}{10} \cdot \frac{3}{3} = 0$

Step 3.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{x}{15}$ by $\frac{2}{2}$ .

$15 - \frac{x \cdot 2}{15 \cdot 2} - \frac{x}{10} \cdot \frac{3}{3} = 0$

Step 3.4.2

Multiply $15$ by $2$ .

$15 - \frac{x \cdot 2}{30} - \frac{x}{10} \cdot \frac{3}{3} = 0$

Step 3.4.3

Multiply $\frac{x}{10}$ by $\frac{3}{3}$ .

$15 - \frac{x \cdot 2}{30} - \frac{x \cdot 3}{10 \cdot 3} = 0$

Step 3.4.4

Multiply $10$ by $3$ .

$15 - \frac{x \cdot 2}{30} - \frac{x \cdot 3}{30} = 0$

Step 3.5

Combine the numerators over the common denominator.

$15 + \frac{- x \cdot 2 - x \cdot 3}{30} = 0$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $x$ out of $- x \cdot 2 - x \cdot 3$ .

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Step 3.6.1.1.1

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

$15 + \frac{x (- 1 \cdot 2) - x \cdot 3}{30} = 0$

Step 3.6.1.1.2

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

$15 + \frac{x (- 1 \cdot 2) + x (- 1 \cdot 3)}{30} = 0$

Step 3.6.1.1.3

Factor $x$ out of $x (- 1 \cdot 2) + x (- 1 \cdot 3)$ .

$15 + \frac{x (- 1 \cdot 2 - 1 \cdot 3)}{30} = 0$

Step 3.6.1.2

Multiply $- 1$ by $2$ .

$15 + \frac{x (- 2 - 1 \cdot 3)}{30} = 0$

Step 3.6.1.3

Multiply $- 1$ by $3$ .

$15 + \frac{x (- 2 - 3)}{30} = 0$

Step 3.6.1.4

Subtract $3$ from $- 2$ .

$15 + \frac{x \cdot - 5}{30} = 0$

Step 3.6.2

Cancel the common factor of $- 5$ and $30$ .

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Step 3.6.2.1

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

$15 + \frac{5 (x \cdot - 1)}{30} = 0$

Step 3.6.2.2

Cancel the common factors.

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Step 3.6.2.2.1

Factor $5$ out of $30$ .

$15 + \frac{5 (x \cdot - 1)}{5 (6)} = 0$

Step 3.6.2.2.2

Cancel the common factor.

$15 + \frac{5 (x \cdot - 1)}{5 \cdot 6} = 0$

Step 3.6.2.2.3

Rewrite the expression.

$15 + \frac{x \cdot - 1}{6} = 0$

Step 3.6.3

Move $- 1$ to the left of $x$ .

$15 + \frac{- 1 \cdot x}{6} = 0$

Step 3.6.4

Move the negative in front of the fraction.

$15 - \frac{x}{6} = 0$

Step 4

Subtract $15$ from both sides of the equation.

$- \frac{x}{6} = - 15$

Step 5

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{x}{6}) = - 6 \cdot - 15$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- 6 (- \frac{x}{6})$ .

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Step 6.1.1.1

Cancel the common factor of $6$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{x}{6}$ into the numerator.

$- 6 \frac{- x}{6} = - 6 \cdot - 15$

Step 6.1.1.1.2

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{- x}{6} = - 6 \cdot - 15$

Step 6.1.1.1.3

Cancel the common factor.

$6 \cdot - 1 \frac{- x}{6} = - 6 \cdot - 15$

Step 6.1.1.1.4

Rewrite the expression.

$- - x = - 6 \cdot - 15$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 6 \cdot - 15$

Step 6.1.1.2.2

Multiply $x$ by $1$ .

$x = - 6 \cdot - 15$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 6$ by $- 15$ .

$x = 90$