Solve 5/6m-5/12=1/8m+2/3

$$\frac { 5 } { 6 } m - \frac { 5 } { 12 } = \frac { 1 } { 8 } m + \frac { 2 } { 3 }$$

Solve for m

$$m = \frac{26}{17} = 1\frac{9}{17} \approx 1.529411765$$

Steps for Solving Linear Equation

Subtract \frac{1}{8}m from both sides.

$$\frac{5}{6}m-\frac{5}{12}-\frac{1}{8}m=\frac{2}{3}$$

Combine \frac{5}{6}m and -\frac{1}{8}m to get \frac{17}{24}m.

$$\frac{17}{24}m-\frac{5}{12}=\frac{2}{3}$$

Add \frac{5}{12} to both sides.

$$\frac{17}{24}m=\frac{2}{3}+\frac{5}{12}$$

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{5}{12} to fractions with denominator 12.

$$\frac{17}{24}m=\frac{8}{12}+\frac{5}{12}$$

Since \frac{8}{12} and \frac{5}{12} have the same denominator, add them by adding their numerators.

$$\frac{17}{24}m=\frac{8+5}{12}$$

Add 8 and 5 to get 13.

$$\frac{17}{24}m=\frac{13}{12}$$

Multiply both sides by \frac{24}{17}, the reciprocal of \frac{17}{24}.

$$m=\frac{13}{12}\times \frac{24}{17}$$

Multiply \frac{13}{12} times \frac{24}{17} by multiplying numerator times numerator and denominator times denominator.

$$m=\frac{13\times 24}{12\times 17}$$

Do the multiplications in the fraction \frac{13\times 24}{12\times 17}.

$$m=\frac{312}{204}$$

Reduce the fraction \frac{312}{204} to lowest terms by extracting and canceling out 12.

$$m=\frac{26}{17}$$