Algebra Examples

$\frac{8}{x} = \frac{2}{3}$

Step 1

Subtract $\frac{2}{3}$ from both sides of the equation.

$\frac{8}{x} - \frac{2}{3} = 0$

Step 2

To write $\frac{8}{x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8}{x} \cdot \frac{3}{3} - \frac{2}{3} = 0$

Step 3

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

$\frac{8}{x} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{x}{x} = 0$

Step 4

Write each expression with a common denominator of $x \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{8}{x}$ by $\frac{3}{3}$ .

$\frac{8 \cdot 3}{x \cdot 3} - \frac{2}{3} \cdot \frac{x}{x} = 0$

Step 4.2

Multiply $\frac{2}{3}$ by $\frac{x}{x}$ .

$\frac{8 \cdot 3}{x \cdot 3} - \frac{2 x}{3 x} = 0$

Step 4.3

Reorder the factors of $x \cdot 3$ .

$\frac{8 \cdot 3}{3 x} - \frac{2 x}{3 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{8 \cdot 3 - 2 x}{3 x} = 0$

Step 6

Simplify the numerator.

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Step 6.1

Factor $2$ out of $8 \cdot 3 - 2 x$ .

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Step 6.1.1

Factor $2$ out of $8 \cdot 3$ .

$\frac{2 (4 \cdot 3) - 2 x}{3 x} = 0$

Step 6.1.2

Factor $2$ out of $- 2 x$ .

$\frac{2 (4 \cdot 3) + 2 (- x)}{3 x} = 0$

Step 6.1.3

Factor $2$ out of $2 (4 \cdot 3) + 2 (- x)$ .

$\frac{2 (4 \cdot 3 - x)}{3 x} = 0$

Step 6.2

Multiply $4$ by $3$ .

$\frac{2 (12 - x)}{3 x} = 0$

Step 7

Set the numerator equal to zero.

$2 (12 - x) = 0$

Step 8

Solve the equation for $x$ .

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Step 8.1

Divide each term in $2 (12 - x) = 0$ by $2$ and simplify.

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Step 8.1.1

Divide each term in $2 (12 - x) = 0$ by $2$ .

$\frac{2 (12 - x)}{2} = \frac{0}{2}$

Step 8.1.2

Simplify the left side.

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Step 8.1.2.1

Cancel the common factor of $2$ .

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Step 8.1.2.1.1

Cancel the common factor.

$\frac{2 (12 - x)}{2} = \frac{0}{2}$

Step 8.1.2.1.2

Divide $12 - x$ by $1$ .

$12 - x = \frac{0}{2}$

Step 8.1.3

Simplify the right side.

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Step 8.1.3.1

Divide $0$ by $2$ .

$12 - x = 0$

Step 8.2

Subtract $12$ from both sides of the equation.

$- x = - 12$

Step 8.3

Divide each term in $- x = - 12$ by $- 1$ and simplify.

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Step 8.3.1

Divide each term in $- x = - 12$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 12}{- 1}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 12}{- 1}$

Step 8.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 12}{- 1}$

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

Divide $- 12$ by $- 1$ .

$x = 12$