Solve 28/3-5/93/10/frac{9frac{1{18}}{frac{27}{6}}}=frac{11+frac{11}{5}}{x}

$$\frac{ \frac{ 28 }{ 3 } - \frac{ 5 }{ 9 } \frac{ 3 }{ 10 } }{ \frac{ 9 \frac{ 1 }{ 18 } }{ \frac{ 27 }{ 6 } } } = \frac{ 11+ \frac{ 11 }{ 5 } }{ x }$$

Solve for x

$$x = \frac{652}{225} = 2\frac{202}{225} \approx 2.897777778$$

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.

$$\frac{81}{163}x\left(\frac{28}{3}-\frac{5}{9}\times \frac{3}{10}\right)=11+\frac{11}{5}$$

Multiply \frac{5}{9} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81}{163}x\left(\frac{28}{3}-\frac{5\times 3}{9\times 10}\right)=11+\frac{11}{5}$$

Do the multiplications in the fraction \frac{5\times 3}{9\times 10}.

$$\frac{81}{163}x\left(\frac{28}{3}-\frac{15}{90}\right)=11+\frac{11}{5}$$

Reduce the fraction \frac{15}{90} to lowest terms by extracting and canceling out 15.

$$\frac{81}{163}x\left(\frac{28}{3}-\frac{1}{6}\right)=11+\frac{11}{5}$$

Least common multiple of 3 and 6 is 6. Convert \frac{28}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{81}{163}x\left(\frac{56}{6}-\frac{1}{6}\right)=11+\frac{11}{5}$$

Since \frac{56}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81}{163}x\times \frac{56-1}{6}=11+\frac{11}{5}$$

Subtract 1 from 56 to get 55.

$$\frac{81}{163}x\times \frac{55}{6}=11+\frac{11}{5}$$

Multiply \frac{81}{163} times \frac{55}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\times 55}{163\times 6}x=11+\frac{11}{5}$$

Do the multiplications in the fraction \frac{81\times 55}{163\times 6}.

$$\frac{4455}{978}x=11+\frac{11}{5}$$

Reduce the fraction \frac{4455}{978} to lowest terms by extracting and canceling out 3.

$$\frac{1485}{326}x=11+\frac{11}{5}$$

Convert 11 to fraction \frac{55}{5}.

$$\frac{1485}{326}x=\frac{55}{5}+\frac{11}{5}$$

Since \frac{55}{5} and \frac{11}{5} have the same denominator, add them by adding their numerators.

$$\frac{1485}{326}x=\frac{55+11}{5}$$

Add 55 and 11 to get 66.

$$\frac{1485}{326}x=\frac{66}{5}$$

Multiply both sides by \frac{326}{1485}, the reciprocal of \frac{1485}{326}.

$$x=\frac{66}{5}\times \frac{326}{1485}$$

Multiply \frac{66}{5} times \frac{326}{1485} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{66\times 326}{5\times 1485}$$

Do the multiplications in the fraction \frac{66\times 326}{5\times 1485}.

$$x=\frac{21516}{7425}$$

Reduce the fraction \frac{21516}{7425} to lowest terms by extracting and canceling out 33.

$$x=\frac{652}{225}$$