Solve (n91.6/760=x/8.314(1/38.95-1/386.8)

$$( n \frac { 91.6 } { 760 } = \frac { x } { 8.314 } ( \frac { 1 } { 38.95 } - \frac { 1 } { 386.8 } )$$

Solve for n

$$n=\frac{869625000x}{37742080591}$$

Steps for Solving Linear Equation

Expand \frac{91.6}{760} by multiplying both numerator and the denominator by 10.

$$n\times \frac{916}{7600}=\frac{x}{8.314}\left(\frac{1}{38.95}-\frac{1}{386.8}\right)$$

Reduce the fraction \frac{916}{7600} to lowest terms by extracting and canceling out 4.

$$n\times \frac{229}{1900}=\frac{x}{8.314}\left(\frac{1}{38.95}-\frac{1}{386.8}\right)$$

Expand \frac{1}{38.95} by multiplying both numerator and the denominator by 100.

$$n\times \frac{229}{1900}=\frac{x}{8.314}\left(\frac{100}{3895}-\frac{1}{386.8}\right)$$

Reduce the fraction \frac{100}{3895} to lowest terms by extracting and canceling out 5.

$$n\times \frac{229}{1900}=\frac{x}{8.314}\left(\frac{20}{779}-\frac{1}{386.8}\right)$$

Expand \frac{1}{386.8} by multiplying both numerator and the denominator by 10.

$$n\times \frac{229}{1900}=\frac{x}{8.314}\left(\frac{20}{779}-\frac{10}{3868}\right)$$

Reduce the fraction \frac{10}{3868} to lowest terms by extracting and canceling out 2.

$$n\times \frac{229}{1900}=\frac{x}{8.314}\left(\frac{20}{779}-\frac{5}{1934}\right)$$

Subtract \frac{5}{1934} from \frac{20}{779} to get \frac{34785}{1506586}.

$$n\times \frac{229}{1900}=\frac{x}{8.314}\times \frac{34785}{1506586}$$

The equation is in standard form.

$$\frac{229}{1900}n=\frac{8696250x}{3131439001}$$

Divide both sides of the equation by \frac{229}{1900}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{229}{1900}n}{\frac{229}{1900}}=\frac{8696250x}{\frac{229}{1900}\times 3131439001}$$

Dividing by \frac{229}{1900} undoes the multiplication by \frac{229}{1900}.

$$n=\frac{8696250x}{\frac{229}{1900}\times 3131439001}$$

Divide \frac{8696250x}{3131439001} by \frac{229}{1900} by multiplying \frac{8696250x}{3131439001} by the reciprocal of \frac{229}{1900}.

$$n=\frac{869625000x}{37742080591}$$

Solve for x

$$x=\frac{37742080591n}{869625000}$$