Solve (7/6-x):x=11/9:1/3

$$( \frac { 7 } { 6 } - x ) : x = \frac { 11 } { 9 } : \frac { 1 } { 3 }$$

Solve for x

$$x=\frac{1}{4}=0.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\frac{7}{6}-x=x\times \frac{\frac{11}{9}}{\frac{1}{3}}$$

Divide \frac{11}{9} by \frac{1}{3} by multiplying \frac{11}{9} by the reciprocal of \frac{1}{3}.

$$\frac{7}{6}-x=x\times \frac{11}{9}\times 3$$

Express \frac{11}{9}\times 3 as a single fraction.

$$\frac{7}{6}-x=x\times \frac{11\times 3}{9}$$

Multiply 11 and 3 to get 33.

$$\frac{7}{6}-x=x\times \frac{33}{9}$$

Reduce the fraction \frac{33}{9} to lowest terms by extracting and canceling out 3.

$$\frac{7}{6}-x=x\times \frac{11}{3}$$

Subtract x\times \frac{11}{3} from both sides.

$$\frac{7}{6}-x-x\times \frac{11}{3}=0$$

Combine -x and -x\times \frac{11}{3} to get -\frac{14}{3}x.

$$\frac{7}{6}-\frac{14}{3}x=0$$

Subtract \frac{7}{6} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{14}{3}x=-\frac{7}{6}$$

Multiply both sides by -\frac{3}{14}, the reciprocal of -\frac{14}{3}.

$$x=-\frac{7}{6}\left(-\frac{3}{14}\right)$$

Multiply -\frac{7}{6} times -\frac{3}{14} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\left(-3\right)}{6\times 14}$$

Do the multiplications in the fraction \frac{-7\left(-3\right)}{6\times 14}.

$$x=\frac{21}{84}$$

Reduce the fraction \frac{21}{84} to lowest terms by extracting and canceling out 21.

$$x=\frac{1}{4}$$