Solve for x 6/7x-1/6=11/14x-6/7

$\frac{6}{7} x - \frac{1}{6} = \frac{11}{14} x - \frac{6}{7}$

Step 1

Combine $\frac{6}{7}$ and $x$ .

$\frac{6 x}{7} - \frac{1}{6} = \frac{11}{14} x - \frac{6}{7}$

Step 2

Combine $\frac{11}{14}$ and $x$ .

$\frac{6 x}{7} - \frac{1}{6} = \frac{11 x}{14} - \frac{6}{7}$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $\frac{11 x}{14}$ from both sides of the equation.

$\frac{6 x}{7} - \frac{1}{6} - \frac{11 x}{14} = - \frac{6}{7}$

To write $\frac{6 x}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{6 x}{7} \cdot \frac{2}{2} - \frac{11 x}{14} - \frac{1}{6} = - \frac{6}{7}$

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6 x}{7}$ by $\frac{2}{2}$ .

$\frac{6 x \cdot 2}{7 \cdot 2} - \frac{11 x}{14} - \frac{1}{6} = - \frac{6}{7}$

Multiply $7$ by $2$ .

$\frac{6 x \cdot 2}{14} - \frac{11 x}{14} - \frac{1}{6} = - \frac{6}{7}$

Combine the numerators over the common denominator.

$\frac{6 x \cdot 2 - 11 x}{14} - \frac{1}{6} = - \frac{6}{7}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $6 x \cdot 2 - 11 x$ .

Factor $x$ out of $6 x \cdot 2$ .

$\frac{x (6 \cdot 2) - 11 x}{14} - \frac{1}{6} = - \frac{6}{7}$

Factor $x$ out of $- 11 x$ .

$\frac{x (6 \cdot 2) + x \cdot - 11}{14} - \frac{1}{6} = - \frac{6}{7}$

Factor $x$ out of $x (6 \cdot 2) + x \cdot - 11$ .

$\frac{x (6 \cdot 2 - 11)}{14} - \frac{1}{6} = - \frac{6}{7}$

Multiply $6$ by $2$ .

$\frac{x (12 - 11)}{14} - \frac{1}{6} = - \frac{6}{7}$

Subtract $11$ from $12$ .

$\frac{x \cdot 1}{14} - \frac{1}{6} = - \frac{6}{7}$

Multiply $x$ by $1$ .

$\frac{x}{14} - \frac{1}{6} = - \frac{6}{7}$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Add $\frac{1}{6}$ to both sides of the equation.

$\frac{x}{14} = - \frac{6}{7} + \frac{1}{6}$

To write $- \frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{x}{14} = - \frac{6}{7} \cdot \frac{6}{6} + \frac{1}{6}$

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{x}{14} = - \frac{6}{7} \cdot \frac{6}{6} + \frac{1}{6} \cdot \frac{7}{7}$

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6}{7}$ by $\frac{6}{6}$ .

$\frac{x}{14} = - \frac{6 \cdot 6}{7 \cdot 6} + \frac{1}{6} \cdot \frac{7}{7}$

Multiply $7$ by $6$ .

$\frac{x}{14} = - \frac{6 \cdot 6}{42} + \frac{1}{6} \cdot \frac{7}{7}$

Multiply $\frac{1}{6}$ by $\frac{7}{7}$ .

$\frac{x}{14} = - \frac{6 \cdot 6}{42} + \frac{7}{6 \cdot 7}$

Multiply $6$ by $7$ .

$\frac{x}{14} = - \frac{6 \cdot 6}{42} + \frac{7}{42}$

Combine the numerators over the common denominator.

$\frac{x}{14} = \frac{- 6 \cdot 6 + 7}{42}$

Simplify the numerator.

Multiply $- 6$ by $6$ .

$\frac{x}{14} = \frac{- 36 + 7}{42}$

Add $- 36$ and $7$ .

$\frac{x}{14} = \frac{- 29}{42}$

Move the negative in front of the fraction.

$\frac{x}{14} = - \frac{29}{42}$

Step 5

Multiply both sides of the equation by $14$ .

$14 \frac{x}{14} = 14 (- \frac{29}{42})$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$14 \frac{x}{14} = 14 (- \frac{29}{42})$

Rewrite the expression.

$x = 14 (- \frac{29}{42})$

Simplify the right side.

Simplify $14 (- \frac{29}{42})$ .

Cancel the common factor of $14$ .

Move the leading negative in $- \frac{29}{42}$ into the numerator.

$x = 14 (\frac{- 29}{42})$

Factor $14$ out of $42$ .

$x = 14 \frac{- 29}{14 (3)}$

Cancel the common factor.

$x = 14 \frac{- 29}{14 \cdot 3}$

Rewrite the expression.

$x = \frac{- 29}{3}$

Move the negative in front of the fraction.

$x = - \frac{29}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{29}{3}$

Decimal Form:

$x = - 9.\overline{6}$

Mixed Number Form:

$x = - 9 \frac{2}{3}$

Solve for x 6/7x-1/6=11/14x-6/7

Related Questions

Support LCMGCF.com by disabling your adblocker.