Solve by Factoring 2/10=11/x

$\frac{2}{10} = \frac{11}{x}$

Step 1

Subtract $\frac{11}{x}$ from both sides of the equation.

$\frac{2}{10} - \frac{11}{x} = 0$

Step 2

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2$ .

$\frac{2 (1)}{10} - \frac{11}{x} = 0$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{2 \cdot 1}{2 \cdot 5} - \frac{11}{x} = 0$

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 5} - \frac{11}{x} = 0$

Rewrite the expression.

$\frac{1}{5} - \frac{11}{x} = 0$

Step 3

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{1}{5} \cdot \frac{x}{x} - \frac{11}{x} = 0$

Step 4

To write $- \frac{11}{x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{5} \cdot \frac{x}{x} - \frac{11}{x} \cdot \frac{5}{5} = 0$

Step 5

Write each expression with a common denominator of $5 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{x}{x}$ .

$\frac{x}{5 x} - \frac{11}{x} \cdot \frac{5}{5} = 0$

Multiply $\frac{11}{x}$ by $\frac{5}{5}$ .

$\frac{x}{5 x} - \frac{11 \cdot 5}{x \cdot 5} = 0$

Reorder the factors of $x \cdot 5$ .

$\frac{x}{5 x} - \frac{11 \cdot 5}{5 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{x - 11 \cdot 5}{5 x} = 0$

Step 7

Multiply $- 11$ by $5$ .

$\frac{x - 55}{5 x} = 0$

Step 8

Set the numerator equal to zero.

$x - 55 = 0$

Step 9

Add $55$ to both sides of the equation.

$x = 55$