Solve 283*(2/15+1/3-7/4*3/14+frac{1}{60}):x=frac{frac{2}{5}-frac{1}{6}}{2-frac{1}{3}*2}:frac{frac{6}{11}*frac{22}{3}-frac{1}{4}}{frac{4}{5}*frac{2}{5}-frac{3}{8}}

$$283 \times ( \frac { 2 } { 15 } + \frac { 1 } { 3 } - \frac { 7 } { 4 } \cdot \frac { 3 } { 14 } + \frac { 1 } { 60 } ) : x = \frac { \frac { 2 } { 5 } - \frac { 1 } { 6 } } { 2 - \frac { 1 } { 3 } \cdot 2 } : \frac { \frac { 6 } { 11 } \cdot \frac { 22 } { 3 } - \frac { 1 } { 4 } } { \frac { 4 } { 5 } \cdot \frac { 2 } { 5 } - \frac { 3 } { 8 } }$$

Solve for x

$$x = -\frac{919750}{77} = -11944\frac{62}{77} \approx -11944.805194805$$

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.

$$283\left(\frac{2}{15}+\frac{1}{3}-\frac{7}{4}\times \frac{3}{14}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Least common multiple of 15 and 3 is 15. Convert \frac{2}{15} and \frac{1}{3} to fractions with denominator 15.

$$283\left(\frac{2}{15}+\frac{5}{15}-\frac{7}{4}\times \frac{3}{14}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Since \frac{2}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$283\left(\frac{2+5}{15}-\frac{7}{4}\times \frac{3}{14}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Add 2 and 5 to get 7.

$$283\left(\frac{7}{15}-\frac{7}{4}\times \frac{3}{14}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Multiply \frac{7}{4} times \frac{3}{14} by multiplying numerator times numerator and denominator times denominator.

$$283\left(\frac{7}{15}-\frac{7\times 3}{4\times 14}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Do the multiplications in the fraction \frac{7\times 3}{4\times 14}.

$$283\left(\frac{7}{15}-\frac{21}{56}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Reduce the fraction \frac{21}{56} to lowest terms by extracting and canceling out 7.

$$283\left(\frac{7}{15}-\frac{3}{8}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Least common multiple of 15 and 8 is 120. Convert \frac{7}{15} and \frac{3}{8} to fractions with denominator 120.

$$283\left(\frac{56}{120}-\frac{45}{120}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Since \frac{56}{120} and \frac{45}{120} have the same denominator, subtract them by subtracting their numerators.

$$283\left(\frac{56-45}{120}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Subtract 45 from 56 to get 11.

$$283\left(\frac{11}{120}+\frac{1}{60}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Least common multiple of 120 and 60 is 120. Convert \frac{11}{120} and \frac{1}{60} to fractions with denominator 120.

$$283\left(\frac{11}{120}+\frac{2}{120}\right)=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Since \frac{11}{120} and \frac{2}{120} have the same denominator, add them by adding their numerators.

$$283\times \frac{11+2}{120}=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Add 11 and 2 to get 13.

$$283\times \frac{13}{120}=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Express 283\times \frac{13}{120} as a single fraction.

$$\frac{283\times 13}{120}=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Multiply 283 and 13 to get 3679.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{\frac{2}{5}-\frac{1}{6}}{2-\frac{1}{3}\times 2}$$

Least common multiple of 5 and 6 is 30. Convert \frac{2}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{\frac{12}{30}-\frac{5}{30}}{2-\frac{1}{3}\times 2}$$

Since \frac{12}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{\frac{12-5}{30}}{2-\frac{1}{3}\times 2}$$

Subtract 5 from 12 to get 7.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{\frac{7}{30}}{2-\frac{1}{3}\times 2}$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{\frac{7}{30}}{2-\frac{2}{3}}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{\frac{7}{30}}{\frac{6}{3}-\frac{2}{3}}$$

Since \frac{6}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{\frac{7}{30}}{\frac{6-2}{3}}$$

Subtract 2 from 6 to get 4.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{\frac{7}{30}}{\frac{4}{3}}$$

Divide \frac{7}{30} by \frac{4}{3} by multiplying \frac{7}{30} by the reciprocal of \frac{4}{3}.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{7}{30}\times \frac{3}{4}$$

Multiply \frac{7}{30} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{7\times 3}{30\times 4}$$

Do the multiplications in the fraction \frac{7\times 3}{30\times 4}.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{21}{120}$$

Reduce the fraction \frac{21}{120} to lowest terms by extracting and canceling out 3.

$$\frac{3679}{120}=-\frac{11}{750}x\times \frac{7}{40}$$

Multiply -\frac{11}{750} times \frac{7}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3679}{120}=\frac{-11\times 7}{750\times 40}x$$

Do the multiplications in the fraction \frac{-11\times 7}{750\times 40}.

$$\frac{3679}{120}=\frac{-77}{30000}x$$

Fraction \frac{-77}{30000} can be rewritten as -\frac{77}{30000} by extracting the negative sign.

$$\frac{3679}{120}=-\frac{77}{30000}x$$

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

$$-\frac{77}{30000}x=\frac{3679}{120}$$

Multiply both sides by -\frac{30000}{77}, the reciprocal of -\frac{77}{30000}.

$$x=\frac{3679}{120}\left(-\frac{30000}{77}\right)$$

Multiply \frac{3679}{120} times -\frac{30000}{77} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{3679\left(-30000\right)}{120\times 77}$$

Do the multiplications in the fraction \frac{3679\left(-30000\right)}{120\times 77}.

$$x=\frac{-110370000}{9240}$$

Reduce the fraction \frac{-110370000}{9240} to lowest terms by extracting and canceling out 120.

$$x=-\frac{919750}{77}$$