Solve for x 2/3+11/12x=1/3

$\frac{2}{3} + \frac{11}{12} x = \frac{1}{3}$

Step 1

Combine $\frac{11}{12}$ and $x$ .

$\frac{2}{3} + \frac{11 x}{12} = \frac{1}{3}$

Step 2

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

Subtract $\frac{2}{3}$ from both sides of the equation.

$\frac{11 x}{12} = \frac{1}{3} - \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{11 x}{12} = \frac{1 - 2}{3}$

Subtract $2$ from $1$ .

$\frac{11 x}{12} = \frac{- 1}{3}$

Move the negative in front of the fraction.

$\frac{11 x}{12} = - \frac{1}{3}$

Step 3

Multiply both sides of the equation by $\frac{12}{11}$ .

$\frac{12}{11} \cdot \frac{11 x}{12} = \frac{12}{11} (- \frac{1}{3})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{11} \cdot \frac{11 x}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{11} \cdot \frac{11 x}{12} = \frac{12}{11} (- \frac{1}{3})$

Rewrite the expression.

$\frac{1}{11} (11 x) = \frac{12}{11} (- \frac{1}{3})$

Cancel the common factor of $11$ .

Factor $11$ out of $11 x$ .

$\frac{1}{11} (11 (x)) = \frac{12}{11} (- \frac{1}{3})$

Cancel the common factor.

$\frac{1}{11} (11 x) = \frac{12}{11} (- \frac{1}{3})$

Rewrite the expression.

$x = \frac{12}{11} (- \frac{1}{3})$

Simplify the right side.

Simplify $\frac{12}{11} (- \frac{1}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$x = \frac{12}{11} \cdot \frac{- 1}{3}$

Factor $3$ out of $12$ .

$x = \frac{3 (4)}{11} \cdot \frac{- 1}{3}$

Cancel the common factor.

$x = \frac{3 \cdot 4}{11} \cdot \frac{- 1}{3}$

Rewrite the expression.

$x = \frac{4}{11} \cdot - 1$

Combine $\frac{4}{11}$ and $- 1$ .

$x = \frac{4 \cdot - 1}{11}$

Simplify the expression.

Multiply $4$ by $- 1$ .

$x = \frac{- 4}{11}$

Move the negative in front of the fraction.

$x = - \frac{4}{11}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{4}{11}$

Decimal Form:

$x = - 0.\overline{36}$

Solve for x 2/3+11/12x=1/3

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