Algebra Examples

$6 \frac{4}{5} = \frac{5}{6} x - 3 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Convert $6 \frac{4}{5}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$6 + \frac{4}{5} = \frac{5}{6} x - 3 \frac{1}{2}$

Step 1.1.2

Add $6$ and $\frac{4}{5}$ .

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Step 1.1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$6 \cdot \frac{5}{5} + \frac{4}{5} = \frac{5}{6} x - 3 \frac{1}{2}$

Step 1.1.2.2

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

$\frac{6 \cdot 5}{5} + \frac{4}{5} = \frac{5}{6} x - 3 \frac{1}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 5 + 4}{5} = \frac{5}{6} x - 3 \frac{1}{2}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $6$ by $5$ .

$\frac{30 + 4}{5} = \frac{5}{6} x - 3 \frac{1}{2}$

Step 1.1.2.4.2

Add $30$ and $4$ .

$\frac{34}{5} = \frac{5}{6} x - 3 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{5}{6} x - 3 \frac{1}{2}$ .

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Step 2.1.1

Convert $3 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{34}{5} = \frac{5}{6} x - (3 + \frac{1}{2})$

Step 2.1.1.2

Add $3$ and $\frac{1}{2}$ .

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Step 2.1.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{34}{5} = \frac{5}{6} x - (3 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.1.1.2.2

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

$\frac{34}{5} = \frac{5}{6} x - (\frac{3 \cdot 2}{2} + \frac{1}{2})$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{34}{5} = \frac{5}{6} x - \frac{3 \cdot 2 + 1}{2}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $3$ by $2$ .

$\frac{34}{5} = \frac{5}{6} x - \frac{6 + 1}{2}$

Step 2.1.1.2.4.2

Add $6$ and $1$ .

$\frac{34}{5} = \frac{5}{6} x - \frac{7}{2}$

Step 2.1.2

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

$\frac{34}{5} = \frac{5 x}{6} - \frac{7}{2}$

Step 3

Rewrite the equation as $\frac{5 x}{6} - \frac{7}{2} = \frac{34}{5}$ .

$\frac{5 x}{6} - \frac{7}{2} = \frac{34}{5}$

Step 4

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

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Step 4.1

Add $\frac{7}{2}$ to both sides of the equation.

$\frac{5 x}{6} = \frac{34}{5} + \frac{7}{2}$

Step 4.2

To write $\frac{34}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{6} = \frac{34}{5} \cdot \frac{2}{2} + \frac{7}{2}$

Step 4.3

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 x}{6} = \frac{34}{5} \cdot \frac{2}{2} + \frac{7}{2} \cdot \frac{5}{5}$

Step 4.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{34}{5}$ by $\frac{2}{2}$ .

$\frac{5 x}{6} = \frac{34 \cdot 2}{5 \cdot 2} + \frac{7}{2} \cdot \frac{5}{5}$

Step 4.4.2

Multiply $5$ by $2$ .

$\frac{5 x}{6} = \frac{34 \cdot 2}{10} + \frac{7}{2} \cdot \frac{5}{5}$

Step 4.4.3

Multiply $\frac{7}{2}$ by $\frac{5}{5}$ .

$\frac{5 x}{6} = \frac{34 \cdot 2}{10} + \frac{7 \cdot 5}{2 \cdot 5}$

Step 4.4.4

Multiply $2$ by $5$ .

$\frac{5 x}{6} = \frac{34 \cdot 2}{10} + \frac{7 \cdot 5}{10}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{5 x}{6} = \frac{34 \cdot 2 + 7 \cdot 5}{10}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $34$ by $2$ .

$\frac{5 x}{6} = \frac{68 + 7 \cdot 5}{10}$

Step 4.6.2

Multiply $7$ by $5$ .

$\frac{5 x}{6} = \frac{68 + 35}{10}$

Step 4.6.3

Add $68$ and $35$ .

$\frac{5 x}{6} = \frac{103}{10}$

Step 5

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

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot \frac{103}{10}$

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

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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

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot \frac{103}{10}$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot \frac{103}{10}$

Step 6.1.1.2

Cancel the common factor of $5$ .

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Step 6.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{6}{5} \cdot \frac{103}{10}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot \frac{103}{10}$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{6}{5} \cdot \frac{103}{10}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{6}{5} \cdot \frac{103}{10}$ .

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Step 6.2.1.1

Cancel the common factor of $2$ .

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Step 6.2.1.1.1

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{5} \cdot \frac{103}{10}$

Step 6.2.1.1.2

Factor $2$ out of $10$ .

$x = \frac{2 \cdot 3}{5} \cdot \frac{103}{2 \cdot 5}$

Step 6.2.1.1.3

Cancel the common factor.

$x = \frac{2 \cdot 3}{5} \cdot \frac{103}{2 \cdot 5}$

Step 6.2.1.1.4

Rewrite the expression.

$x = \frac{3}{5} \cdot \frac{103}{5}$

Step 6.2.1.2

Multiply $\frac{3}{5}$ by $\frac{103}{5}$ .

$x = \frac{3 \cdot 103}{5 \cdot 5}$

Step 6.2.1.3

Multiply.

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Step 6.2.1.3.1

Multiply $3$ by $103$ .

$x = \frac{309}{5 \cdot 5}$

Step 6.2.1.3.2

Multiply $5$ by $5$ .

$x = \frac{309}{25}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{309}{25}$

Decimal Form:

$x = 12.36$

Mixed Number Form:

$x = 12 \frac{9}{25}$