Solve (-21/3x-1/2):(-11/2)=-1/3:(-2)

$$( - 2 \frac { 1 } { 3 } x - \frac { 1 } { 2 } ) : ( - 1 \frac { 1 } { 2 } ) = - \frac { 1 } { 3 } : ( - 2 )$$

Solve for x

$$x=-\frac{3}{28}\approx -0.107142857$$

Steps for Solving Linear Equation

Multiply 2 and 3 to get 6.

$$\frac{\left(-\frac{6+1}{3}\right)x-\frac{1}{2}}{-\frac{1\times 2+1}{2}}=\frac{-\frac{1}{3}}{-2}$$

Add 6 and 1 to get 7.

$$\frac{-\frac{7}{3}x-\frac{1}{2}}{-\frac{1\times 2+1}{2}}=\frac{-\frac{1}{3}}{-2}$$

Multiply 1 and 2 to get 2.

$$\frac{-\frac{7}{3}x-\frac{1}{2}}{-\frac{2+1}{2}}=\frac{-\frac{1}{3}}{-2}$$

Add 2 and 1 to get 3.

$$\frac{-\frac{7}{3}x-\frac{1}{2}}{-\frac{3}{2}}=\frac{-\frac{1}{3}}{-2}$$

Express \frac{-\frac{1}{3}}{-2} as a single fraction.

$$\frac{-\frac{7}{3}x-\frac{1}{2}}{-\frac{3}{2}}=\frac{-1}{3\left(-2\right)}$$

Multiply 3 and -2 to get -6.

$$\frac{-\frac{7}{3}x-\frac{1}{2}}{-\frac{3}{2}}=\frac{-1}{-6}$$

Fraction \frac{-1}{-6} can be simplified to \frac{1}{6} by removing the negative sign from both the numerator and the denominator.

$$\frac{-\frac{7}{3}x-\frac{1}{2}}{-\frac{3}{2}}=\frac{1}{6}$$

Divide each term of -\frac{7}{3}x-\frac{1}{2} by -\frac{3}{2} to get \frac{-\frac{7}{3}x}{-\frac{3}{2}}+\frac{-\frac{1}{2}}{-\frac{3}{2}}.

$$\frac{-\frac{7}{3}x}{-\frac{3}{2}}+\frac{-\frac{1}{2}}{-\frac{3}{2}}=\frac{1}{6}$$

Divide -\frac{7}{3}x by -\frac{3}{2} to get \frac{14}{9}x.

$$\frac{14}{9}x+\frac{-\frac{1}{2}}{-\frac{3}{2}}=\frac{1}{6}$$

Divide -\frac{1}{2} by -\frac{3}{2} by multiplying -\frac{1}{2} by the reciprocal of -\frac{3}{2}.

$$\frac{14}{9}x-\frac{1}{2}\left(-\frac{2}{3}\right)=\frac{1}{6}$$

Multiply -\frac{1}{2} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14}{9}x+\frac{-\left(-2\right)}{2\times 3}=\frac{1}{6}$$

Do the multiplications in the fraction \frac{-\left(-2\right)}{2\times 3}.

$$\frac{14}{9}x+\frac{2}{6}=\frac{1}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{14}{9}x+\frac{1}{3}=\frac{1}{6}$$

Subtract \frac{1}{3} from both sides.

$$\frac{14}{9}x=\frac{1}{6}-\frac{1}{3}$$

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

$$\frac{14}{9}x=\frac{1}{6}-\frac{2}{6}$$

Since \frac{1}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14}{9}x=\frac{1-2}{6}$$

Subtract 2 from 1 to get -1.

$$\frac{14}{9}x=-\frac{1}{6}$$

Multiply both sides by \frac{9}{14}, the reciprocal of \frac{14}{9}.

$$x=-\frac{1}{6}\times \frac{9}{14}$$

Multiply -\frac{1}{6} times \frac{9}{14} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9}{6\times 14}$$

Do the multiplications in the fraction \frac{-9}{6\times 14}.

$$x=\frac{-9}{84}$$

Reduce the fraction \frac{-9}{84} to lowest terms by extracting and canceling out 3.

$$x=-\frac{3}{28}$$