Algebra Examples

$\frac{4}{3} (x - \frac{5}{6}) = \frac{62}{9}$

Step 1

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} (\frac{4}{3} \cdot (x - \frac{5}{6})) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3}{4} (\frac{4}{3} \cdot (x - \frac{5}{6}))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{4} (\frac{4}{3} x + \frac{4}{3} (- \frac{5}{6})) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.2

Combine $\frac{4}{3}$ and $x$ .

$\frac{3}{4} (\frac{4 x}{3} + \frac{4}{3} (- \frac{5}{6})) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{3}{4} (\frac{4 x}{3} + \frac{4}{3} \cdot \frac{- 5}{6}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.3.2

Factor $2$ out of $4$ .

$\frac{3}{4} (\frac{4 x}{3} + \frac{2 (2)}{3} \cdot \frac{- 5}{6}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.3.3

Factor $2$ out of $6$ .

$\frac{3}{4} (\frac{4 x}{3} + \frac{2 \cdot 2}{3} \cdot \frac{- 5}{2 \cdot 3}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.3.4

Cancel the common factor.

$\frac{3}{4} (\frac{4 x}{3} + \frac{2 \cdot 2}{3} \cdot \frac{- 5}{2 \cdot 3}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.3.5

Rewrite the expression.

$\frac{3}{4} (\frac{4 x}{3} + \frac{2}{3} \cdot \frac{- 5}{3}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.4

Multiply $\frac{2}{3}$ by $\frac{- 5}{3}$ .

$\frac{3}{4} (\frac{4 x}{3} + \frac{2 \cdot - 5}{3 \cdot 3}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.5

Simplify the expression.

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Step 2.1.1.5.1

Multiply $2$ by $- 5$ .

$\frac{3}{4} (\frac{4 x}{3} + \frac{- 10}{3 \cdot 3}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.5.2

Multiply $3$ by $3$ .

$\frac{3}{4} (\frac{4 x}{3} + \frac{- 10}{9}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.5.3

Move the negative in front of the fraction.

$\frac{3}{4} (\frac{4 x}{3} - \frac{10}{9}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.6

Apply the distributive property.

$\frac{3}{4} \cdot \frac{4 x}{3} + \frac{3}{4} (- \frac{10}{9}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 x}{3} + \frac{3}{4} (- \frac{10}{9}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.7.2

Rewrite the expression.

$\frac{1}{4} (4 x) + \frac{3}{4} (- \frac{10}{9}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.8

Cancel the common factor of $4$ .

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Step 2.1.1.8.1

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) + \frac{3}{4} (- \frac{10}{9}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.8.2

Cancel the common factor.

$\frac{1}{4} (4 x) + \frac{3}{4} (- \frac{10}{9}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.8.3

Rewrite the expression.

$x + \frac{3}{4} (- \frac{10}{9}) = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.9

Cancel the common factor of $3$ .

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Step 2.1.1.9.1

Move the leading negative in $- \frac{10}{9}$ into the numerator.

$x + \frac{3}{4} \cdot \frac{- 10}{9} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.9.2

Factor $3$ out of $9$ .

$x + \frac{3}{4} \cdot \frac{- 10}{3 (3)} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.9.3

Cancel the common factor.

$x + \frac{3}{4} \cdot \frac{- 10}{3 \cdot 3} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.9.4

Rewrite the expression.

$x + \frac{1}{4} \cdot \frac{- 10}{3} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.10

Cancel the common factor of $2$ .

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Step 2.1.1.10.1

Factor $2$ out of $4$ .

$x + \frac{1}{2 (2)} \cdot \frac{- 10}{3} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.10.2

Factor $2$ out of $- 10$ .

$x + \frac{1}{2 \cdot 2} \cdot \frac{2 \cdot - 5}{3} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.10.3

Cancel the common factor.

$x + \frac{1}{2 \cdot 2} \cdot \frac{2 \cdot - 5}{3} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.10.4

Rewrite the expression.

$x + \frac{1}{2} \cdot \frac{- 5}{3} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.11

Multiply $\frac{1}{2}$ by $\frac{- 5}{3}$ .

$x + \frac{- 5}{2 \cdot 3} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.12

Simplify the expression.

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Step 2.1.1.12.1

Multiply $2$ by $3$ .

$x + \frac{- 5}{6} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.1.1.12.2

Move the negative in front of the fraction.

$x - \frac{5}{6} = \frac{3}{4} \cdot \frac{62}{9}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{4} \cdot \frac{62}{9}$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Factor $3$ out of $9$ .

$x - \frac{5}{6} = \frac{3}{4} \cdot \frac{62}{3 (3)}$

Step 2.2.1.1.2

Cancel the common factor.

$x - \frac{5}{6} = \frac{3}{4} \cdot \frac{62}{3 \cdot 3}$

Step 2.2.1.1.3

Rewrite the expression.

$x - \frac{5}{6} = \frac{1}{4} \cdot \frac{62}{3}$

Step 2.2.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.2.1

Factor $2$ out of $4$ .

$x - \frac{5}{6} = \frac{1}{2 (2)} \cdot \frac{62}{3}$

Step 2.2.1.2.2

Factor $2$ out of $62$ .

$x - \frac{5}{6} = \frac{1}{2 \cdot 2} \cdot \frac{2 \cdot 31}{3}$

Step 2.2.1.2.3

Cancel the common factor.

$x - \frac{5}{6} = \frac{1}{2 \cdot 2} \cdot \frac{2 \cdot 31}{3}$

Step 2.2.1.2.4

Rewrite the expression.

$x - \frac{5}{6} = \frac{1}{2} \cdot \frac{31}{3}$

Step 2.2.1.3

Multiply $\frac{1}{2}$ by $\frac{31}{3}$ .

$x - \frac{5}{6} = \frac{31}{2 \cdot 3}$

Step 2.2.1.4

Multiply $2$ by $3$ .

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

Step 3

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

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Step 3.1

Add $\frac{5}{6}$ to both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Add $31$ and $5$ .

$x = \frac{36}{6}$

Step 3.4

Divide $36$ by $6$ .

$x = 6$