Solve (11/9-x):x=17/3:34/5

$$( \frac { 11 } { 9 } - x ) : x = \frac { 17 } { 3 } : \frac { 34 } { 5 }$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

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.

$$\frac{11}{9}-x=x\times \frac{\frac{17}{3}}{\frac{34}{5}}$$

Divide \frac{17}{3} by \frac{34}{5} by multiplying \frac{17}{3} by the reciprocal of \frac{34}{5}.

$$\frac{11}{9}-x=x\times \frac{17}{3}\times \frac{5}{34}$$

Multiply \frac{17}{3} times \frac{5}{34} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{9}-x=x\times \frac{17\times 5}{3\times 34}$$

Do the multiplications in the fraction \frac{17\times 5}{3\times 34}.

$$\frac{11}{9}-x=x\times \frac{85}{102}$$

Reduce the fraction \frac{85}{102} to lowest terms by extracting and canceling out 17.

$$\frac{11}{9}-x=x\times \frac{5}{6}$$

Subtract x\times \frac{5}{6} from both sides.

$$\frac{11}{9}-x-x\times \frac{5}{6}=0$$

Combine -x and -x\times \frac{5}{6} to get -\frac{11}{6}x.

$$\frac{11}{9}-\frac{11}{6}x=0$$

Subtract \frac{11}{9} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{11}{6}x=-\frac{11}{9}$$

Multiply both sides by -\frac{6}{11}, the reciprocal of -\frac{11}{6}.

$$x=-\frac{11}{9}\left(-\frac{6}{11}\right)$$

Multiply -\frac{11}{9} times -\frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-11\left(-6\right)}{9\times 11}$$

Do the multiplications in the fraction \frac{-11\left(-6\right)}{9\times 11}.

$$x=\frac{66}{99}$$

Reduce the fraction \frac{66}{99} to lowest terms by extracting and canceling out 33.

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