Solve by Factoring 9/x=1/2

$\frac{9}{x} = \frac{1}{2}$

Step 1

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{9}{x} - \frac{1}{2} = 0$

Step 2

To write $\frac{9}{x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{x} \cdot \frac{2}{2} - \frac{1}{2} = 0$

Step 3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{9}{x} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{x}{x} = 0$

Step 4

Write each expression with a common denominator of $x \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9}{x}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{x \cdot 2} - \frac{1}{2} \cdot \frac{x}{x} = 0$

Multiply $\frac{1}{2}$ by $\frac{x}{x}$ .

$\frac{9 \cdot 2}{x \cdot 2} - \frac{x}{2 x} = 0$

Reorder the factors of $x \cdot 2$ .

$\frac{9 \cdot 2}{2 x} - \frac{x}{2 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{9 \cdot 2 - x}{2 x} = 0$

Step 6

Multiply $9$ by $2$ .

$\frac{18 - x}{2 x} = 0$

Step 7

Set the numerator equal to zero.

$18 - x = 0$

Step 8

Solve the equation for $x$ .

Subtract $18$ from both sides of the equation.

$- x = - 18$

Divide each term in $- x = - 18$ by $- 1$ and simplify.

Divide each term in $- x = - 18$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 18}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 18}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 1}$

Simplify the right side.

Divide $- 18$ by $- 1$ .

$x = 18$