Finite Math Examples

$\frac{5}{6} x - \frac{1}{2} = 2$

Step 1

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

$\frac{5 x}{6} - \frac{1}{2} = 2$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{5 x}{6} = 2 + \frac{1}{2}$

Step 2.2

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

$\frac{5 x}{6} = 2 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.3

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

$\frac{5 x}{6} = \frac{2 \cdot 2}{2} + \frac{1}{2}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 x}{6} = \frac{2 \cdot 2 + 1}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $2$ .

$\frac{5 x}{6} = \frac{4 + 1}{2}$

Step 2.5.2

Add $4$ and $1$ .

$\frac{5 x}{6} = \frac{5}{2}$

Step 3

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot \frac{5}{2}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{6}{5} \cdot \frac{5 x}{6}$ .

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Step 4.1.1.1

Cancel the common factor of $6$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot \frac{5}{2}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot \frac{5}{2}$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{6}{5} \cdot \frac{5}{2}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot \frac{5}{2}$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{6}{5} \cdot \frac{5}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{6}{5} \cdot \frac{5}{2}$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $6$ .

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

Step 4.2.1.1.2

Cancel the common factor.

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

Step 4.2.1.1.3

Rewrite the expression.

$x = \frac{3}{5} \cdot 5$

Step 4.2.1.2

Cancel the common factor of $5$ .

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Step 4.2.1.2.1

Cancel the common factor.

$x = \frac{3}{5} \cdot 5$

Step 4.2.1.2.2

Rewrite the expression.

$x = 3$