Solve by Factoring 11/(2x)-2/(3x)=1/6

$\frac{11}{2 x} - \frac{2}{3 x} = \frac{1}{6}$

Step 1

Subtract $\frac{1}{6}$ from both sides of the equation.

$\frac{11}{2 x} - \frac{2}{3 x} - \frac{1}{6} = 0$

Step 2

Simplify $\frac{11}{2 x} - \frac{2}{3 x} - \frac{1}{6}$ .

To write $\frac{11}{2 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11}{2 x} \cdot \frac{3}{3} - \frac{2}{3 x} - \frac{1}{6} = 0$

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

$\frac{11}{2 x} \cdot \frac{3}{3} - \frac{2}{3 x} \cdot \frac{2}{2} - \frac{1}{6} = 0$

Write each expression with a common denominator of $6 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{11}{2 x}$ by $\frac{3}{3}$ .

$\frac{11 \cdot 3}{2 x \cdot 3} - \frac{2}{3 x} \cdot \frac{2}{2} - \frac{1}{6} = 0$

Multiply $3$ by $2$ .

$\frac{11 \cdot 3}{6 x} - \frac{2}{3 x} \cdot \frac{2}{2} - \frac{1}{6} = 0$

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

$\frac{11 \cdot 3}{6 x} - \frac{2 \cdot 2}{3 x \cdot 2} - \frac{1}{6} = 0$

Multiply $2$ by $3$ .

$\frac{11 \cdot 3}{6 x} - \frac{2 \cdot 2}{6 x} - \frac{1}{6} = 0$

Combine the numerators over the common denominator.

$\frac{11 \cdot 3 - 2 \cdot 2}{6 x} - \frac{1}{6} = 0$

Simplify the numerator.

Multiply $11$ by $3$ .

$\frac{33 - 2 \cdot 2}{6 x} - \frac{1}{6} = 0$

Multiply $- 2$ by $2$ .

$\frac{33 - 4}{6 x} - \frac{1}{6} = 0$

Subtract $4$ from $33$ .

$\frac{29}{6 x} - \frac{1}{6} = 0$

Step 3

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{29}{6 x} - \frac{1}{6} \cdot \frac{x}{x} = 0$

Step 4

Multiply $\frac{1}{6}$ by $\frac{x}{x}$ .

$\frac{29}{6 x} - \frac{x}{6 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{29 - x}{6 x} = 0$

Step 6

Set the numerator equal to zero.

$29 - x = 0$

Step 7

Solve the equation for $x$ .

Subtract $29$ from both sides of the equation.

$- x = - 29$

Divide each term in $- x = - 29$ by $- 1$ and simplify.

Divide each term in $- x = - 29$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 29}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 29}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 29}{- 1}$

Simplify the right side.

Divide $- 29$ by $- 1$ .

$x = 29$

Solve by Factoring 11/(2x)-2/(3x)=1/6

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