Solve x:(10+7/3)=(4/9+2/3-2/5):(1-frac{2}{15}+frac{7}{9})

$$x : ( 10 + \frac { 7 } { 3 } ) = ( \frac { 4 } { 9 } + \frac { 2 } { 3 } - \frac { 2 } { 5 } ) : ( 1 - \frac { 2 } { 15 } + \frac { 7 } { 9 } )$$

Solve for x

$$x = \frac{16}{3} = 5\frac{1}{3} \approx 5.333333333$$

Steps for Solving Linear Equation

Convert 10 to fraction \frac{30}{3}.

$$\frac{x}{\frac{30}{3}+\frac{7}{3}}=\frac{\frac{4}{9}+\frac{2}{3}-\frac{2}{5}}{1-\frac{2}{15}+\frac{7}{9}}$$

Since \frac{30}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{30+7}{3}}=\frac{\frac{4}{9}+\frac{2}{3}-\frac{2}{5}}{1-\frac{2}{15}+\frac{7}{9}}$$

Add 30 and 7 to get 37.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{4}{9}+\frac{2}{3}-\frac{2}{5}}{1-\frac{2}{15}+\frac{7}{9}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{2}{3} to fractions with denominator 9.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{4}{9}+\frac{6}{9}-\frac{2}{5}}{1-\frac{2}{15}+\frac{7}{9}}$$

Since \frac{4}{9} and \frac{6}{9} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{4+6}{9}-\frac{2}{5}}{1-\frac{2}{15}+\frac{7}{9}}$$

Add 4 and 6 to get 10.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{10}{9}-\frac{2}{5}}{1-\frac{2}{15}+\frac{7}{9}}$$

Least common multiple of 9 and 5 is 45. Convert \frac{10}{9} and \frac{2}{5} to fractions with denominator 45.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{50}{45}-\frac{18}{45}}{1-\frac{2}{15}+\frac{7}{9}}$$

Since \frac{50}{45} and \frac{18}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{50-18}{45}}{1-\frac{2}{15}+\frac{7}{9}}$$

Subtract 18 from 50 to get 32.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{32}{45}}{1-\frac{2}{15}+\frac{7}{9}}$$

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

$$\frac{x}{\frac{37}{3}}=\frac{\frac{32}{45}}{\frac{15}{15}-\frac{2}{15}+\frac{7}{9}}$$

Since \frac{15}{15} and \frac{2}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{32}{45}}{\frac{15-2}{15}+\frac{7}{9}}$$

Subtract 2 from 15 to get 13.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{32}{45}}{\frac{13}{15}+\frac{7}{9}}$$

Least common multiple of 15 and 9 is 45. Convert \frac{13}{15} and \frac{7}{9} to fractions with denominator 45.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{32}{45}}{\frac{39}{45}+\frac{35}{45}}$$

Since \frac{39}{45} and \frac{35}{45} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{32}{45}}{\frac{39+35}{45}}$$

Add 39 and 35 to get 74.

$$\frac{x}{\frac{37}{3}}=\frac{\frac{32}{45}}{\frac{74}{45}}$$

Divide \frac{32}{45} by \frac{74}{45} by multiplying \frac{32}{45} by the reciprocal of \frac{74}{45}.

$$\frac{x}{\frac{37}{3}}=\frac{32}{45}\times \frac{45}{74}$$

Multiply \frac{32}{45} times \frac{45}{74} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{37}{3}}=\frac{32\times 45}{45\times 74}$$

Cancel out 45 in both numerator and denominator.

$$\frac{x}{\frac{37}{3}}=\frac{32}{74}$$

Reduce the fraction \frac{32}{74} to lowest terms by extracting and canceling out 2.

$$\frac{x}{\frac{37}{3}}=\frac{16}{37}$$

Multiply both sides by \frac{37}{3}.

$$x=\frac{16}{37}\times \frac{37}{3}$$

Multiply \frac{16}{37} times \frac{37}{3} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{16\times 37}{37\times 3}$$

Cancel out 37 in both numerator and denominator.

$$x=\frac{16}{3}$$