Solve (3-1/2)*1/12/(3-7):1-frac{7/10}{6,2}=(frac{4}{3}*frac{5}{6}):x

$$\frac { ( 3 - \frac { 1 } { 2 } ) \cdot \frac { 1 } { 12 } } { ( 3 - 7 ) } : \frac { 1 - \frac { 7 } { 10 } } { 6,2 } = ( \frac { 4 } { 3 } \cdot \frac { 5 } { 6 } ) : x$$

Solve for x

$$x=-\frac{32}{31}\approx -1,032258065$$

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.

$$\frac{62}{3}x\times \frac{\left(3-\frac{1}{2}\right)\times \frac{1}{12}}{3-7}=\frac{4}{3}\times \frac{5}{6}$$

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

$$\frac{62}{3}x\times \frac{\left(\frac{6}{2}-\frac{1}{2}\right)\times \frac{1}{12}}{3-7}=\frac{4}{3}\times \frac{5}{6}$$

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

$$\frac{62}{3}x\times \frac{\frac{6-1}{2}\times \frac{1}{12}}{3-7}=\frac{4}{3}\times \frac{5}{6}$$

Subtract 1 from 6 to get 5.

$$\frac{62}{3}x\times \frac{\frac{5}{2}\times \frac{1}{12}}{3-7}=\frac{4}{3}\times \frac{5}{6}$$

Multiply \frac{5}{2} times \frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{62}{3}x\times \frac{\frac{5\times 1}{2\times 12}}{3-7}=\frac{4}{3}\times \frac{5}{6}$$

Do the multiplications in the fraction \frac{5\times 1}{2\times 12}.

$$\frac{62}{3}x\times \frac{\frac{5}{24}}{3-7}=\frac{4}{3}\times \frac{5}{6}$$

Subtract 7 from 3 to get -4.

$$\frac{62}{3}x\times \frac{\frac{5}{24}}{-4}=\frac{4}{3}\times \frac{5}{6}$$

Express \frac{\frac{5}{24}}{-4} as a single fraction.

$$\frac{62}{3}x\times \frac{5}{24\left(-4\right)}=\frac{4}{3}\times \frac{5}{6}$$

Multiply 24 and -4 to get -96.

$$\frac{62}{3}x\times \frac{5}{-96}=\frac{4}{3}\times \frac{5}{6}$$

Fraction \frac{5}{-96} can be rewritten as -\frac{5}{96} by extracting the negative sign.

$$\frac{62}{3}x\left(-\frac{5}{96}\right)=\frac{4}{3}\times \frac{5}{6}$$

Multiply \frac{62}{3} times -\frac{5}{96} by multiplying numerator times numerator and denominator times denominator.

$$\frac{62\left(-5\right)}{3\times 96}x=\frac{4}{3}\times \frac{5}{6}$$

Do the multiplications in the fraction \frac{62\left(-5\right)}{3\times 96}.

$$\frac{-310}{288}x=\frac{4}{3}\times \frac{5}{6}$$

Reduce the fraction \frac{-310}{288} to lowest terms by extracting and canceling out 2.

$$-\frac{155}{144}x=\frac{4}{3}\times \frac{5}{6}$$

Multiply \frac{4}{3} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{155}{144}x=\frac{4\times 5}{3\times 6}$$

Do the multiplications in the fraction \frac{4\times 5}{3\times 6}.

$$-\frac{155}{144}x=\frac{20}{18}$$

Reduce the fraction \frac{20}{18} to lowest terms by extracting and canceling out 2.

$$-\frac{155}{144}x=\frac{10}{9}$$

Multiply both sides by -\frac{144}{155}, the reciprocal of -\frac{155}{144}.

$$x=\frac{10}{9}\left(-\frac{144}{155}\right)$$

Multiply \frac{10}{9} times -\frac{144}{155} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{10\left(-144\right)}{9\times 155}$$

Do the multiplications in the fraction \frac{10\left(-144\right)}{9\times 155}.

$$x=\frac{-1440}{1395}$$

Reduce the fraction \frac{-1440}{1395} to lowest terms by extracting and canceling out 45.

$$x=-\frac{32}{31}$$