Solve x:(4+1/6/frac{1{3}-1/12})=[26/9*(frac{8}{15}-frac{2}{5})]:(frac{1-frac{11}{15}}{3}+frac{1}{5})

$$x : ( \frac { 4 + \frac { 1 } { 6 } } { \frac { 1 } { 3 } - \frac { 1 } { 12 } } ) = [ \frac { 26 } { 9 } \cdot ( \frac { 8 } { 15 } - \frac { 2 } { 5 } ) ] : ( \frac { 1 - \frac { 11 } { 15 } } { 3 } + \frac { 1 } { 5 } )$$

Solve for x

$$x = \frac{200}{9} = 22\frac{2}{9} \approx 22.222222222$$

Steps for Solving Linear Equation

Divide x by \frac{4+\frac{1}{6}}{\frac{1}{3}-\frac{1}{12}} by multiplying x by the reciprocal of \frac{4+\frac{1}{6}}{\frac{1}{3}-\frac{1}{12}}.

$$\frac{x\left(\frac{1}{3}-\frac{1}{12}\right)}{4+\frac{1}{6}}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{2}{5}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Least common multiple of 3 and 12 is 12. Convert \frac{1}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{x\left(\frac{4}{12}-\frac{1}{12}\right)}{4+\frac{1}{6}}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{2}{5}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Since \frac{4}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times \frac{4-1}{12}}{4+\frac{1}{6}}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{2}{5}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Subtract 1 from 4 to get 3.

$$\frac{x\times \frac{3}{12}}{4+\frac{1}{6}}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{2}{5}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

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

$$\frac{x\times \frac{1}{4}}{4+\frac{1}{6}}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{2}{5}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Convert 4 to fraction \frac{24}{6}.

$$\frac{x\times \frac{1}{4}}{\frac{24}{6}+\frac{1}{6}}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{2}{5}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Since \frac{24}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{x\times \frac{1}{4}}{\frac{24+1}{6}}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{2}{5}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Add 24 and 1 to get 25.

$$\frac{x\times \frac{1}{4}}{\frac{25}{6}}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{2}{5}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Divide x\times \frac{1}{4} by \frac{25}{6} to get x\times \frac{3}{50}.

$$x\times \frac{3}{50}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{2}{5}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Least common multiple of 15 and 5 is 15. Convert \frac{8}{15} and \frac{2}{5} to fractions with denominator 15.

$$x\times \frac{3}{50}=\frac{\frac{26}{9}\left(\frac{8}{15}-\frac{6}{15}\right)}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Since \frac{8}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$x\times \frac{3}{50}=\frac{\frac{26}{9}\times \frac{8-6}{15}}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Subtract 6 from 8 to get 2.

$$x\times \frac{3}{50}=\frac{\frac{26}{9}\times \frac{2}{15}}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Multiply \frac{26}{9} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$x\times \frac{3}{50}=\frac{\frac{26\times 2}{9\times 15}}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Do the multiplications in the fraction \frac{26\times 2}{9\times 15}.

$$x\times \frac{3}{50}=\frac{\frac{52}{135}}{\frac{1-\frac{11}{15}}{3}+\frac{1}{5}}$$

Convert 1 to fraction \frac{15}{15}.

$$x\times \frac{3}{50}=\frac{\frac{52}{135}}{\frac{\frac{15}{15}-\frac{11}{15}}{3}+\frac{1}{5}}$$

Since \frac{15}{15} and \frac{11}{15} have the same denominator, subtract them by subtracting their numerators.

$$x\times \frac{3}{50}=\frac{\frac{52}{135}}{\frac{\frac{15-11}{15}}{3}+\frac{1}{5}}$$

Subtract 11 from 15 to get 4.

$$x\times \frac{3}{50}=\frac{\frac{52}{135}}{\frac{\frac{4}{15}}{3}+\frac{1}{5}}$$

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

$$x\times \frac{3}{50}=\frac{\frac{52}{135}}{\frac{4}{15\times 3}+\frac{1}{5}}$$

Multiply 15 and 3 to get 45.

$$x\times \frac{3}{50}=\frac{\frac{52}{135}}{\frac{4}{45}+\frac{1}{5}}$$

Least common multiple of 45 and 5 is 45. Convert \frac{4}{45} and \frac{1}{5} to fractions with denominator 45.

$$x\times \frac{3}{50}=\frac{\frac{52}{135}}{\frac{4}{45}+\frac{9}{45}}$$

Since \frac{4}{45} and \frac{9}{45} have the same denominator, add them by adding their numerators.

$$x\times \frac{3}{50}=\frac{\frac{52}{135}}{\frac{4+9}{45}}$$

Add 4 and 9 to get 13.

$$x\times \frac{3}{50}=\frac{\frac{52}{135}}{\frac{13}{45}}$$

Divide \frac{52}{135} by \frac{13}{45} by multiplying \frac{52}{135} by the reciprocal of \frac{13}{45}.

$$x\times \frac{3}{50}=\frac{52}{135}\times \frac{45}{13}$$

Multiply \frac{52}{135} times \frac{45}{13} by multiplying numerator times numerator and denominator times denominator.

$$x\times \frac{3}{50}=\frac{52\times 45}{135\times 13}$$

Do the multiplications in the fraction \frac{52\times 45}{135\times 13}.

$$x\times \frac{3}{50}=\frac{2340}{1755}$$

Reduce the fraction \frac{2340}{1755} to lowest terms by extracting and canceling out 585.

$$x\times \frac{3}{50}=\frac{4}{3}$$

Multiply both sides by \frac{50}{3}, the reciprocal of \frac{3}{50}.

$$x=\frac{4}{3}\times \frac{50}{3}$$

Multiply \frac{4}{3} times \frac{50}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{4\times 50}{3\times 3}$$

Do the multiplications in the fraction \frac{4\times 50}{3\times 3}.

$$x=\frac{200}{9}$$