Solve 4/5m-1/3=5/7

$$\frac { 4 } { 5 } m - \frac { 1 } { 3 } = \frac { 5 } { 7 }$$

Solve for m

$$m = \frac{55}{42} = 1\frac{13}{42} \approx 1.30952381$$

Steps for Solving Linear Equation

Add \frac{1}{3} to both sides.

$$\frac{4}{5}m=\frac{5}{7}+\frac{1}{3}$$

Least common multiple of 7 and 3 is 21. Convert \frac{5}{7} and \frac{1}{3} to fractions with denominator 21.

$$\frac{4}{5}m=\frac{15}{21}+\frac{7}{21}$$

Since \frac{15}{21} and \frac{7}{21} have the same denominator, add them by adding their numerators.

$$\frac{4}{5}m=\frac{15+7}{21}$$

Add 15 and 7 to get 22.

$$\frac{4}{5}m=\frac{22}{21}$$

Multiply both sides by \frac{5}{4}, the reciprocal of \frac{4}{5}.

$$m=\frac{22}{21}\times \frac{5}{4}$$

Multiply \frac{22}{21} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$m=\frac{22\times 5}{21\times 4}$$

Do the multiplications in the fraction \frac{22\times 5}{21\times 4}.

$$m=\frac{110}{84}$$

Reduce the fraction \frac{110}{84} to lowest terms by extracting and canceling out 2.

$$m=\frac{55}{42}$$