Solve (x-21/3*(-31/7)*(-22/11)/1frac{1{9}*(-1frac{1}{8})*16}):(-frac{1}{3})=6

$$( x - \frac { 2 \frac { 1 } { 3 } \cdot ( - 3 \frac { 1 } { 7 } ) \cdot ( - 2 \frac { 2 } { 11 } ) } { 1 \frac { 1 } { 9 } \cdot ( - 1 \frac { 1 } { 8 } ) \cdot 16 } ) : ( - \frac { 1 } { 3 } ) = 6$$

Solve for x

$$x = -\frac{14}{5} = -2\frac{4}{5} = -2.8$$

Steps for Solving Linear Equation

Multiply both sides by -\frac{1}{3}.

$$x-\frac{\frac{2\times 3+1}{3}\left(-\frac{3\times 7+1}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Multiply 2 and 3 to get 6.

$$x-\frac{\frac{6+1}{3}\left(-\frac{3\times 7+1}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Add 6 and 1 to get 7.

$$x-\frac{\frac{7}{3}\left(-\frac{3\times 7+1}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Multiply 3 and 7 to get 21.

$$x-\frac{\frac{7}{3}\left(-\frac{21+1}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Add 21 and 1 to get 22.

$$x-\frac{\frac{7}{3}\left(-\frac{22}{7}\right)\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Multiply \frac{7}{3} times -\frac{22}{7} by multiplying numerator times numerator and denominator times denominator.

$$x-\frac{\frac{7\left(-22\right)}{3\times 7}\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Cancel out 7 in both numerator and denominator.

$$x-\frac{\frac{-22}{3}\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Fraction \frac{-22}{3} can be rewritten as -\frac{22}{3} by extracting the negative sign.

$$x-\frac{-\frac{22}{3}\left(-\frac{2\times 11+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Multiply 2 and 11 to get 22.

$$x-\frac{-\frac{22}{3}\left(-\frac{22+2}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Add 22 and 2 to get 24.

$$x-\frac{-\frac{22}{3}\left(-\frac{24}{11}\right)}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Multiply -\frac{22}{3} times -\frac{24}{11} by multiplying numerator times numerator and denominator times denominator.

$$x-\frac{\frac{-22\left(-24\right)}{3\times 11}}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Do the multiplications in the fraction \frac{-22\left(-24\right)}{3\times 11}.

$$x-\frac{\frac{528}{33}}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Divide 528 by 33 to get 16.

$$x-\frac{16}{\frac{1\times 9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Multiply 1 and 9 to get 9.

$$x-\frac{16}{\frac{9+1}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Add 9 and 1 to get 10.

$$x-\frac{16}{\frac{10}{9}\left(-\frac{1\times 8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Multiply 1 and 8 to get 8.

$$x-\frac{16}{\frac{10}{9}\left(-\frac{8+1}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Add 8 and 1 to get 9.

$$x-\frac{16}{\frac{10}{9}\left(-\frac{9}{8}\right)\times 16}=6\left(-\frac{1}{3}\right)$$

Multiply \frac{10}{9} times -\frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$x-\frac{16}{\frac{10\left(-9\right)}{9\times 8}\times 16}=6\left(-\frac{1}{3}\right)$$

Do the multiplications in the fraction \frac{10\left(-9\right)}{9\times 8}.

$$x-\frac{16}{\frac{-90}{72}\times 16}=6\left(-\frac{1}{3}\right)$$

Reduce the fraction \frac{-90}{72} to lowest terms by extracting and canceling out 18.

$$x-\frac{16}{-\frac{5}{4}\times 16}=6\left(-\frac{1}{3}\right)$$

Express -\frac{5}{4}\times 16 as a single fraction.

$$x-\frac{16}{\frac{-5\times 16}{4}}=6\left(-\frac{1}{3}\right)$$

Multiply -5 and 16 to get -80.

$$x-\frac{16}{\frac{-80}{4}}=6\left(-\frac{1}{3}\right)$$

Divide -80 by 4 to get -20.

$$x-\frac{16}{-20}=6\left(-\frac{1}{3}\right)$$

Reduce the fraction \frac{16}{-20} to lowest terms by extracting and canceling out 4.

$$x-\left(-\frac{4}{5}\right)=6\left(-\frac{1}{3}\right)$$

The opposite of -\frac{4}{5} is \frac{4}{5}.

$$x+\frac{4}{5}=6\left(-\frac{1}{3}\right)$$

Express 6\left(-\frac{1}{3}\right) as a single fraction.

$$x+\frac{4}{5}=\frac{6\left(-1\right)}{3}$$

Multiply 6 and -1 to get -6.

$$x+\frac{4}{5}=\frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$x+\frac{4}{5}=-2$$

Subtract \frac{4}{5} from both sides.

$$x=-2-\frac{4}{5}$$

Convert -2 to fraction -\frac{10}{5}.

$$x=-\frac{10}{5}-\frac{4}{5}$$

Since -\frac{10}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{-10-4}{5}$$

Subtract 4 from -10 to get -14.

$$x=-\frac{14}{5}$$