Solve (11/12-3/12):(3/2*1/2)=x:[(frac{1}{15}+frac{4}{20})*3]

$$( \frac { 11 } { 12 } - \frac { 3 } { 12 } ) : ( \frac { 3 } { 2 } \times \frac { 1 } { 2 } ) = x : [ ( \frac { 1 } { 15 } + \frac { 4 } { 20 } ) \times 3 ]$$

Solve for x

$$x=\frac{32}{45}\approx 0.711111111$$

Steps for Solving Linear Equation

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{11}{12}-\frac{1}{4}}{\frac{3}{2}\times \frac{1}{2}}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Least common multiple of 12 and 4 is 12. Convert \frac{11}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{11}{12}-\frac{3}{12}}{\frac{3}{2}\times \frac{1}{2}}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Since \frac{11}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11-3}{12}}{\frac{3}{2}\times \frac{1}{2}}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Subtract 3 from 11 to get 8.

$$\frac{\frac{8}{12}}{\frac{3}{2}\times \frac{1}{2}}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{2}{3}}{\frac{3}{2}\times \frac{1}{2}}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Multiply \frac{3}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2}{3}}{\frac{3\times 1}{2\times 2}}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Do the multiplications in the fraction \frac{3\times 1}{2\times 2}.

$$\frac{\frac{2}{3}}{\frac{3}{4}}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Divide \frac{2}{3} by \frac{3}{4} by multiplying \frac{2}{3} by the reciprocal of \frac{3}{4}.

$$\frac{2}{3}\times \frac{4}{3}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Multiply \frac{2}{3} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 4}{3\times 3}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Do the multiplications in the fraction \frac{2\times 4}{3\times 3}.

$$\frac{8}{9}=\frac{x}{\left(\frac{1}{15}+\frac{4}{20}\right)\times 3}$$

Reduce the fraction \frac{4}{20} to lowest terms by extracting and canceling out 4.

$$\frac{8}{9}=\frac{x}{\left(\frac{1}{15}+\frac{1}{5}\right)\times 3}$$

Least common multiple of 15 and 5 is 15. Convert \frac{1}{15} and \frac{1}{5} to fractions with denominator 15.

$$\frac{8}{9}=\frac{x}{\left(\frac{1}{15}+\frac{3}{15}\right)\times 3}$$

Since \frac{1}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{8}{9}=\frac{x}{\frac{1+3}{15}\times 3}$$

Add 1 and 3 to get 4.

$$\frac{8}{9}=\frac{x}{\frac{4}{15}\times 3}$$

Express \frac{4}{15}\times 3 as a single fraction.

$$\frac{8}{9}=\frac{x}{\frac{4\times 3}{15}}$$

Multiply 4 and 3 to get 12.

$$\frac{8}{9}=\frac{x}{\frac{12}{15}}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{8}{9}=\frac{x}{\frac{4}{5}}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x}{\frac{4}{5}}=\frac{8}{9}$$

Multiply both sides by \frac{4}{5}.

$$x=\frac{8}{9}\times \frac{4}{5}$$

Multiply \frac{8}{9} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{8\times 4}{9\times 5}$$

Do the multiplications in the fraction \frac{8\times 4}{9\times 5}.

$$x=\frac{32}{45}$$