Solve by Factoring 1/3+4/x=5/9

$\frac{1}{3} + \frac{4}{x} = \frac{5}{9}$

Step 1

Subtract $\frac{5}{9}$ from both sides of the equation.

$\frac{1}{3} + \frac{4}{x} - \frac{5}{9} = 0$

Step 2

Simplify $\frac{1}{3} + \frac{4}{x} - \frac{5}{9}$ .

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4}{x} + \frac{1}{3} \cdot \frac{3}{3} - \frac{5}{9} = 0$

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

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

$\frac{4}{x} + \frac{3}{3 \cdot 3} - \frac{5}{9} = 0$

Multiply $3$ by $3$ .

$\frac{4}{x} + \frac{3}{9} - \frac{5}{9} = 0$

Combine the numerators over the common denominator.

$\frac{4}{x} + \frac{3 - 5}{9} = 0$

Subtract $5$ from $3$ .

$\frac{4}{x} + \frac{- 2}{9} = 0$

Move the negative in front of the fraction.

$\frac{4}{x} - \frac{2}{9} = 0$

Step 3

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

$\frac{4}{x} \cdot \frac{9}{9} - \frac{2}{9} = 0$

Step 4

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

$\frac{4}{x} \cdot \frac{9}{9} - \frac{2}{9} \cdot \frac{x}{x} = 0$

Step 5

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

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

$\frac{4 \cdot 9}{x \cdot 9} - \frac{2}{9} \cdot \frac{x}{x} = 0$

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

$\frac{4 \cdot 9}{x \cdot 9} - \frac{2 x}{9 x} = 0$

Reorder the factors of $x \cdot 9$ .

$\frac{4 \cdot 9}{9 x} - \frac{2 x}{9 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{4 \cdot 9 - 2 x}{9 x} = 0$

Step 7

Simplify the numerator.

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

Factor $2$ out of $4 \cdot 9$ .

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

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

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

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

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

Multiply $2$ by $9$ .

$\frac{2 (18 - x)}{9 x} = 0$

Step 8

Set the numerator equal to zero.

$2 (18 - x) = 0$

Step 9

Solve the equation for $x$ .

Divide each term in $2 (18 - x) = 0$ by $2$ and simplify.

Divide each term in $2 (18 - x) = 0$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $18 - x$ by $1$ .

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

Simplify the right side.

Divide $0$ by $2$ .

$18 - x = 0$

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 $- 1$ .

$x = 18$

Solve by Factoring 1/3+4/x=5/9

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