Finite Math Examples

$\frac{x}{6} - \frac{x}{7} = \frac{5}{6}$

Step 1

Simplify $\frac{x}{6} - \frac{x}{7}$ .

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Step 1.1

To write $\frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{x}{6} \cdot \frac{7}{7} - \frac{x}{7} = \frac{5}{6}$

Step 1.2

To write $- \frac{x}{7}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x}{6} \cdot \frac{7}{7} - \frac{x}{7} \cdot \frac{6}{6} = \frac{5}{6}$

Step 1.3

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{6}$ by $\frac{7}{7}$ .

$\frac{x \cdot 7}{6 \cdot 7} - \frac{x}{7} \cdot \frac{6}{6} = \frac{5}{6}$

Step 1.3.2

Multiply $6$ by $7$ .

$\frac{x \cdot 7}{42} - \frac{x}{7} \cdot \frac{6}{6} = \frac{5}{6}$

Step 1.3.3

Multiply $\frac{x}{7}$ by $\frac{6}{6}$ .

$\frac{x \cdot 7}{42} - \frac{x \cdot 6}{7 \cdot 6} = \frac{5}{6}$

Step 1.3.4

Multiply $7$ by $6$ .

$\frac{x \cdot 7}{42} - \frac{x \cdot 6}{42} = \frac{5}{6}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 7 - x \cdot 6}{42} = \frac{5}{6}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $x$ out of $x \cdot 7 - x \cdot 6$ .

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Step 1.5.1.1

Factor $x$ out of $x \cdot 7$ .

$\frac{x (7) - x \cdot 6}{42} = \frac{5}{6}$

Step 1.5.1.2

Factor $x$ out of $- x \cdot 6$ .

$\frac{x (7) + x (- 1 \cdot 6)}{42} = \frac{5}{6}$

Step 1.5.1.3

Factor $x$ out of $x (7) + x (- 1 \cdot 6)$ .

$\frac{x (7 - 1 \cdot 6)}{42} = \frac{5}{6}$

Step 1.5.2

Multiply $- 1$ by $6$ .

$\frac{x (7 - 6)}{42} = \frac{5}{6}$

Step 1.5.3

Subtract $6$ from $7$ .

$\frac{x \cdot 1}{42} = \frac{5}{6}$

Step 1.6

Multiply $x$ by $1$ .

$\frac{x}{42} = \frac{5}{6}$

Step 2

Multiply both sides of the equation by $42$ .

$42 \frac{x}{42} = 42 (\frac{5}{6})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $42$ .

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Step 3.1.1.1

Cancel the common factor.

$42 \frac{x}{42} = 42 (\frac{5}{6})$

Step 3.1.1.2

Rewrite the expression.

$x = 42 (\frac{5}{6})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $42 (\frac{5}{6})$ .

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Step 3.2.1.1

Cancel the common factor of $6$ .

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Step 3.2.1.1.1

Factor $6$ out of $42$ .

$x = 6 (7) \frac{5}{6}$

Step 3.2.1.1.2

Cancel the common factor.

$x = 6 \cdot 7 \frac{5}{6}$

Step 3.2.1.1.3

Rewrite the expression.

$x = 7 \cdot 5$

Step 3.2.1.2

Multiply $7$ by $5$ .

$x = 35$