Finite Math Examples

$\frac{x}{5} = \frac{x}{6} - 9$

Step 1

Multiply both sides by $5$ .

$\frac{x}{5} \cdot 5 = (\frac{x}{6} - 9) \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x}{5} \cdot 5 = (\frac{x}{6} - 9) \cdot 5$

Step 2.1.1.2

Rewrite the expression.

$x = (\frac{x}{6} - 9) \cdot 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{x}{6} - 9) \cdot 5$ .

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Step 2.2.1.1

Simplify terms.

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Step 2.2.1.1.1

Apply the distributive property.

$x = \frac{x}{6} \cdot 5 - 9 \cdot 5$

Step 2.2.1.1.2

Combine $\frac{x}{6}$ and $5$ .

$x = \frac{x \cdot 5}{6} - 9 \cdot 5$

Step 2.2.1.1.3

Multiply $- 9$ by $5$ .

$x = \frac{x \cdot 5}{6} - 45$

Step 2.2.1.2

Move $5$ to the left of $x$ .

$x = \frac{5 x}{6} - 45$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $\frac{5 x}{6}$ from both sides of the equation.

$x - \frac{5 x}{6} = - 45$

Step 3.1.2

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

$x \cdot \frac{6}{6} - \frac{5 x}{6} = - 45$

Step 3.1.3

Combine $x$ and $\frac{6}{6}$ .

$\frac{x \cdot 6}{6} - \frac{5 x}{6} = - 45$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 6 - 5 x}{6} = - 45$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Move $6$ to the left of $x$ .

$\frac{6 \cdot x - 5 x}{6} = - 45$

Step 3.1.5.2

Subtract $5 x$ from $6 x$ .

$\frac{x}{6} = - 45$

Step 3.2

Multiply both sides of the equation by $6$ .

$6 \frac{x}{6} = 6 \cdot - 45$

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Cancel the common factor of $6$ .

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Step 3.3.1.1.1

Cancel the common factor.

$6 \frac{x}{6} = 6 \cdot - 45$

Step 3.3.1.1.2

Rewrite the expression.

$x = 6 \cdot - 45$

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Multiply $6$ by $- 45$ .

$x = - 270$