Algebra Examples

$\frac{x}{3} - \frac{5}{6} = \frac{3 (x - 3)}{12}$

Step 1

Cancel the common factors.

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Step 1.1

Factor $3$ out of $12$ .

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

Step 1.2

Cancel the common factor.

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

Step 1.3

Rewrite the expression.

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

Step 2

Multiply both sides by $4$ .

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

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

Simplify terms.

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Step 3.1.1.1.1

Apply the distributive property.

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

Step 3.1.1.1.2

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

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

Step 3.1.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.1.3.1

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

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

Step 3.1.1.1.3.2

Factor $2$ out of $6$ .

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

Step 3.1.1.1.3.3

Factor $2$ out of $4$ .

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

Step 3.1.1.1.3.4

Cancel the common factor.

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

Step 3.1.1.1.3.5

Rewrite the expression.

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

Step 3.1.1.1.4

Combine $\frac{- 5}{3}$ and $2$ .

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

Step 3.1.1.1.5

Multiply $- 5$ by $2$ .

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

Step 3.1.1.2

Simplify each term.

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Step 3.1.1.2.1

Move $4$ to the left of $x$ .

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

Step 3.1.1.2.2

Move the negative in front of the fraction.

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

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

$\frac{4 x}{3} - \frac{10}{3} = x - 3$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $x$ from both sides of the equation.

$\frac{4 x}{3} - \frac{10}{3} - x = - 3$

Step 4.1.2

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

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

Step 4.1.3

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

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

Step 4.1.4

Combine the numerators over the common denominator.

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

Step 4.1.5

Combine the numerators over the common denominator.

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

Step 4.1.6

Multiply $3$ by $- 1$ .

$\frac{4 x - 3 x - 10}{3} = - 3$

Step 4.1.7

Subtract $3 x$ from $4 x$ .

$\frac{x - 10}{3} = - 3$

Step 4.2

Multiply both sides of the equation by $3$ .

$3 \frac{x - 10}{3} = 3 \cdot - 3$

Step 4.3

Simplify both sides of the equation.

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Step 4.3.1

Simplify the left side.

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Step 4.3.1.1

Cancel the common factor of $3$ .

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Step 4.3.1.1.1

Cancel the common factor.

$3 \frac{x - 10}{3} = 3 \cdot - 3$

Step 4.3.1.1.2

Rewrite the expression.

$x - 10 = 3 \cdot - 3$

Step 4.3.2

Simplify the right side.

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Step 4.3.2.1

Multiply $3$ by $- 3$ .

$x - 10 = - 9$

Step 4.4

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

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Step 4.4.1

Add $10$ to both sides of the equation.

$x = - 9 + 10$

Step 4.4.2

Add $- 9$ and $10$ .

$x = 1$