Solve by Factoring 4/9=10/x

$\frac{4}{9} = \frac{10}{x}$

Step 1

Subtract $\frac{10}{x}$ from both sides of the equation.

$\frac{4}{9} - \frac{10}{x} = 0$

Step 2

To write $\frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{4}{9} \cdot \frac{x}{x} - \frac{10}{x} = 0$

Step 3

To write $- \frac{10}{x}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{4}{9} \cdot \frac{x}{x} - \frac{10}{x} \cdot \frac{9}{9} = 0$

Step 4

Write each expression with a common denominator of $9 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{9}$ by $\frac{x}{x}$ .

$\frac{4 x}{9 x} - \frac{10}{x} \cdot \frac{9}{9} = 0$

Multiply $\frac{10}{x}$ by $\frac{9}{9}$ .

$\frac{4 x}{9 x} - \frac{10 \cdot 9}{x \cdot 9} = 0$

Reorder the factors of $x \cdot 9$ .

$\frac{4 x}{9 x} - \frac{10 \cdot 9}{9 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{4 x - 10 \cdot 9}{9 x} = 0$

Step 6

Simplify the numerator.

Factor $2$ out of $4 x - 10 \cdot 9$ .

Factor $2$ out of $4 x$ .

$\frac{2 (2 x) - 10 \cdot 9}{9 x} = 0$

Factor $2$ out of $- 10 \cdot 9$ .

$\frac{2 (2 x) + 2 (- 5 \cdot 9)}{9 x} = 0$

Factor $2$ out of $2 (2 x) + 2 (- 5 \cdot 9)$ .

$\frac{2 (2 x - 5 \cdot 9)}{9 x} = 0$

Multiply $- 5$ by $9$ .

$\frac{2 (2 x - 45)}{9 x} = 0$

Step 7

Set the numerator equal to zero.

$2 (2 x - 45) = 0$

Step 8

Solve the equation for $x$ .

Divide each term in $2 (2 x - 45) = 0$ by $2$ and simplify.

Divide each term in $2 (2 x - 45) = 0$ by $2$ .

$\frac{2 (2 x - 45)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (2 x - 45)}{2} = \frac{0}{2}$

Divide $2 x - 45$ by $1$ .

$2 x - 45 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$2 x - 45 = 0$

Add $45$ to both sides of the equation.

$2 x = 45$

Divide each term in $2 x = 45$ by $2$ and simplify.

Divide each term in $2 x = 45$ by $2$ .

$\frac{2 x}{2} = \frac{45}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{45}{2}$

Divide $x$ by $1$ .

$x = \frac{45}{2}$

Solve by Factoring 4/9=10/x

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