Solve 3/5=3/4n-8/7

$$\frac { 3 } { 5 } = \frac { 3 } { 4 } n - \frac { 8 } { 7 }$$

Solve for n

$$n = \frac{244}{105} = 2\frac{34}{105} \approx 2.323809524$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{4}n-\frac{8}{7}=\frac{3}{5}$$

Add \frac{8}{7} to both sides.

$$\frac{3}{4}n=\frac{3}{5}+\frac{8}{7}$$

Least common multiple of 5 and 7 is 35. Convert \frac{3}{5} and \frac{8}{7} to fractions with denominator 35.

$$\frac{3}{4}n=\frac{21}{35}+\frac{40}{35}$$

Since \frac{21}{35} and \frac{40}{35} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}n=\frac{21+40}{35}$$

Add 21 and 40 to get 61.

$$\frac{3}{4}n=\frac{61}{35}$$

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$n=\frac{61}{35}\times \frac{4}{3}$$

Multiply \frac{61}{35} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$n=\frac{61\times 4}{35\times 3}$$

Do the multiplications in the fraction \frac{61\times 4}{35\times 3}.

$$n=\frac{244}{105}$$