Solve xdiv(16/25div2/15-6/5)=(5/8+frac{1}{3}divfrac{6}{5})div(frac{7}{12}-frac{1}{4}+frac{1}{3})=

$$x \div ( \frac{ 16 }{ 25 } \div \frac { 2 } { 15 } - \frac { 6 } { 5 } )=( \frac{ 5 }{ 8 } + \frac{ 1 }{ 3 } \div \frac { 6 } { 5 } ) \div ( \frac{ 7 }{ 12 } - \frac{ 1 }{ 4 } + \frac{ 1 }{ 3 } )=$$

Solve for x

$$x = \frac{39}{8} = 4\frac{7}{8} = 4.875$$

Steps for Solving Linear Equation

Divide \frac{16}{25} by \frac{2}{15} by multiplying \frac{16}{25} by the reciprocal of \frac{2}{15}.

$$\frac{x}{\frac{16}{25}\times \frac{15}{2}-\frac{6}{5}}=\frac{\frac{5}{8}+\frac{\frac{1}{3}}{\frac{6}{5}}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Multiply \frac{16}{25} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{16\times 15}{25\times 2}-\frac{6}{5}}=\frac{\frac{5}{8}+\frac{\frac{1}{3}}{\frac{6}{5}}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Do the multiplications in the fraction \frac{16\times 15}{25\times 2}.

$$\frac{x}{\frac{240}{50}-\frac{6}{5}}=\frac{\frac{5}{8}+\frac{\frac{1}{3}}{\frac{6}{5}}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Reduce the fraction \frac{240}{50} to lowest terms by extracting and canceling out 10.

$$\frac{x}{\frac{24}{5}-\frac{6}{5}}=\frac{\frac{5}{8}+\frac{\frac{1}{3}}{\frac{6}{5}}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Since \frac{24}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{24-6}{5}}=\frac{\frac{5}{8}+\frac{\frac{1}{3}}{\frac{6}{5}}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Subtract 6 from 24 to get 18.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{5}{8}+\frac{\frac{1}{3}}{\frac{6}{5}}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Divide \frac{1}{3} by \frac{6}{5} by multiplying \frac{1}{3} by the reciprocal of \frac{6}{5}.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{5}{8}+\frac{1}{3}\times \frac{5}{6}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Multiply \frac{1}{3} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{5}{8}+\frac{1\times 5}{3\times 6}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Do the multiplications in the fraction \frac{1\times 5}{3\times 6}.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{5}{8}+\frac{5}{18}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Least common multiple of 8 and 18 is 72. Convert \frac{5}{8} and \frac{5}{18} to fractions with denominator 72.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{45}{72}+\frac{20}{72}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Since \frac{45}{72} and \frac{20}{72} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{45+20}{72}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Add 45 and 20 to get 65.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{65}{72}}{\frac{7}{12}-\frac{1}{4}+\frac{1}{3}}$$

Least common multiple of 12 and 4 is 12. Convert \frac{7}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{65}{72}}{\frac{7}{12}-\frac{3}{12}+\frac{1}{3}}$$

Since \frac{7}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{65}{72}}{\frac{7-3}{12}+\frac{1}{3}}$$

Subtract 3 from 7 to get 4.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{65}{72}}{\frac{4}{12}+\frac{1}{3}}$$

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

$$\frac{x}{\frac{18}{5}}=\frac{\frac{65}{72}}{\frac{1}{3}+\frac{1}{3}}$$

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

$$\frac{x}{\frac{18}{5}}=\frac{\frac{65}{72}}{\frac{1+1}{3}}$$

Add 1 and 1 to get 2.

$$\frac{x}{\frac{18}{5}}=\frac{\frac{65}{72}}{\frac{2}{3}}$$

Divide \frac{65}{72} by \frac{2}{3} by multiplying \frac{65}{72} by the reciprocal of \frac{2}{3}.

$$\frac{x}{\frac{18}{5}}=\frac{65}{72}\times \frac{3}{2}$$

Multiply \frac{65}{72} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{\frac{18}{5}}=\frac{65\times 3}{72\times 2}$$

Do the multiplications in the fraction \frac{65\times 3}{72\times 2}.

$$\frac{x}{\frac{18}{5}}=\frac{195}{144}$$

Reduce the fraction \frac{195}{144} to lowest terms by extracting and canceling out 3.

$$\frac{x}{\frac{18}{5}}=\frac{65}{48}$$

Multiply both sides by \frac{18}{5}.

$$x=\frac{65}{48}\times \frac{18}{5}$$

Multiply \frac{65}{48} times \frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{65\times 18}{48\times 5}$$

Do the multiplications in the fraction \frac{65\times 18}{48\times 5}.

$$x=\frac{1170}{240}$$

Reduce the fraction \frac{1170}{240} to lowest terms by extracting and canceling out 30.

$$x=\frac{39}{8}$$