Solve (28/3-5/9*3/10):(9*1/18:frac{27}{6})=(11+frac{11}{5}):x

$$( \frac { 28 } { 3 } - \frac { 5 } { 9 } \cdot \frac { 3 } { 10 } ) : ( 9 \cdot \frac { 1 } { 18 } : \frac { 27 } { 6 } ) = ( 11 + \frac { 11 } { 5 } ) : x$$

Solve for x

$$x=\frac{4}{25}=0.16$$

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.

$$9x\left(\frac{28}{3}-\frac{5}{9}\times \frac{3}{10}\right)=11+\frac{11}{5}$$

Multiply \frac{5}{9} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$9x\left(\frac{28}{3}-\frac{5\times 3}{9\times 10}\right)=11+\frac{11}{5}$$

Do the multiplications in the fraction \frac{5\times 3}{9\times 10}.

$$9x\left(\frac{28}{3}-\frac{15}{90}\right)=11+\frac{11}{5}$$

Reduce the fraction \frac{15}{90} to lowest terms by extracting and canceling out 15.

$$9x\left(\frac{28}{3}-\frac{1}{6}\right)=11+\frac{11}{5}$$

Least common multiple of 3 and 6 is 6. Convert \frac{28}{3} and \frac{1}{6} to fractions with denominator 6.

$$9x\left(\frac{56}{6}-\frac{1}{6}\right)=11+\frac{11}{5}$$

Since \frac{56}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$9x\times \frac{56-1}{6}=11+\frac{11}{5}$$

Subtract 1 from 56 to get 55.

$$9x\times \frac{55}{6}=11+\frac{11}{5}$$

Express 9\times \frac{55}{6} as a single fraction.

$$\frac{9\times 55}{6}x=11+\frac{11}{5}$$

Multiply 9 and 55 to get 495.

$$\frac{495}{6}x=11+\frac{11}{5}$$

Reduce the fraction \frac{495}{6} to lowest terms by extracting and canceling out 3.

$$\frac{165}{2}x=11+\frac{11}{5}$$

Convert 11 to fraction \frac{55}{5}.

$$\frac{165}{2}x=\frac{55}{5}+\frac{11}{5}$$

Since \frac{55}{5} and \frac{11}{5} have the same denominator, add them by adding their numerators.

$$\frac{165}{2}x=\frac{55+11}{5}$$

Add 55 and 11 to get 66.

$$\frac{165}{2}x=\frac{66}{5}$$

Multiply both sides by \frac{2}{165}, the reciprocal of \frac{165}{2}.

$$x=\frac{66}{5}\times \frac{2}{165}$$

Multiply \frac{66}{5} times \frac{2}{165} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{66\times 2}{5\times 165}$$

Do the multiplications in the fraction \frac{66\times 2}{5\times 165}.

$$x=\frac{132}{825}$$

Reduce the fraction \frac{132}{825} to lowest terms by extracting and canceling out 33.

$$x=\frac{4}{25}$$