Solve 3/4m-1/3=1/2-5/6m

$$\frac { 3 } { 4 } m - \frac { 1 } { 3 } = \frac { 1 } { 2 } - \frac { 5 } { 6 } m$$

Solve for m

$$m=\frac{10}{19}\approx 0.526315789$$

Steps for Solving Linear Equation

Add \frac{5}{6}m to both sides.

$$\frac{3}{4}m-\frac{1}{3}+\frac{5}{6}m=\frac{1}{2}$$

Combine \frac{3}{4}m and \frac{5}{6}m to get \frac{19}{12}m.

$$\frac{19}{12}m-\frac{1}{3}=\frac{1}{2}$$

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

$$\frac{19}{12}m=\frac{1}{2}+\frac{1}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{19}{12}m=\frac{3}{6}+\frac{2}{6}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{19}{12}m=\frac{3+2}{6}$$

Add 3 and 2 to get 5.

$$\frac{19}{12}m=\frac{5}{6}$$

Multiply both sides by \frac{12}{19}, the reciprocal of \frac{19}{12}.

$$m=\frac{5}{6}\times \frac{12}{19}$$

Multiply \frac{5}{6} times \frac{12}{19} by multiplying numerator times numerator and denominator times denominator.

$$m=\frac{5\times 12}{6\times 19}$$

Do the multiplications in the fraction \frac{5\times 12}{6\times 19}.

$$m=\frac{60}{114}$$

Reduce the fraction \frac{60}{114} to lowest terms by extracting and canceling out 6.

$$m=\frac{10}{19}$$