Precalculus Examples

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

Step 1

Rewrite the equation as $\frac{5}{6} x - \frac{4}{5} = \frac{3}{4}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

Add $\frac{4}{5}$ to both sides of the equation.

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

Step 3.2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 3.3

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 3.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{3}{4}$ by $\frac{5}{5}$ .

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

Step 3.4.2

Multiply $4$ by $5$ .

$\frac{5 x}{6} = \frac{3 \cdot 5}{20} + \frac{4}{5} \cdot \frac{4}{4}$

Step 3.4.3

Multiply $\frac{4}{5}$ by $\frac{4}{4}$ .

$\frac{5 x}{6} = \frac{3 \cdot 5}{20} + \frac{4 \cdot 4}{5 \cdot 4}$

Step 3.4.4

Multiply $5$ by $4$ .

$\frac{5 x}{6} = \frac{3 \cdot 5}{20} + \frac{4 \cdot 4}{20}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{5 x}{6} = \frac{3 \cdot 5 + 4 \cdot 4}{20}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $3$ by $5$ .

$\frac{5 x}{6} = \frac{15 + 4 \cdot 4}{20}$

Step 3.6.2

Multiply $4$ by $4$ .

$\frac{5 x}{6} = \frac{15 + 16}{20}$

Step 3.6.3

Add $15$ and $16$ .

$\frac{5 x}{6} = \frac{31}{20}$

Step 4

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

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot \frac{31}{20}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Cancel the common factor of $6$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot \frac{31}{20}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot \frac{31}{20}$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{6}{5} \cdot \frac{31}{20}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot \frac{31}{20}$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{6}{5} \cdot \frac{31}{20}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{6}{5} \cdot \frac{31}{20}$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{5} \cdot \frac{31}{20}$

Step 5.2.1.1.2

Factor $2$ out of $20$ .

$x = \frac{2 \cdot 3}{5} \cdot \frac{31}{2 \cdot 10}$

Step 5.2.1.1.3

Cancel the common factor.

$x = \frac{2 \cdot 3}{5} \cdot \frac{31}{2 \cdot 10}$

Step 5.2.1.1.4

Rewrite the expression.

$x = \frac{3}{5} \cdot \frac{31}{10}$

Step 5.2.1.2

Multiply $\frac{3}{5}$ by $\frac{31}{10}$ .

$x = \frac{3 \cdot 31}{5 \cdot 10}$

Step 5.2.1.3

Multiply.

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Step 5.2.1.3.1

Multiply $3$ by $31$ .

$x = \frac{93}{5 \cdot 10}$

Step 5.2.1.3.2

Multiply $5$ by $10$ .

$x = \frac{93}{50}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{93}{50}$

Decimal Form:

$x = 1.86$

Mixed Number Form:

$x = 1 \frac{43}{50}$