Solve 5/6m-5/12=7/8m+2/3

$$\frac { 5 } { 6 } m - \frac { 5 } { 12 } = \frac { 7 } { 8 } m + \frac { 2 } { 3 }$$

Solve for m

$$m=-26$$

Steps for Solving Linear Equation

Subtract \frac{7}{8}m from both sides.

$$\frac{5}{6}m-\frac{5}{12}-\frac{7}{8}m=\frac{2}{3}$$

Combine \frac{5}{6}m and -\frac{7}{8}m to get -\frac{1}{24}m.

$$-\frac{1}{24}m-\frac{5}{12}=\frac{2}{3}$$

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

$$-\frac{1}{24}m=\frac{2}{3}+\frac{5}{12}$$

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

$$-\frac{1}{24}m=\frac{8}{12}+\frac{5}{12}$$

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

$$-\frac{1}{24}m=\frac{8+5}{12}$$

Add 8 and 5 to get 13.

$$-\frac{1}{24}m=\frac{13}{12}$$

Multiply both sides by -24, the reciprocal of -\frac{1}{24}.

$$m=\frac{13}{12}\left(-24\right)$$

Express \frac{13}{12}\left(-24\right) as a single fraction.

$$m=\frac{13\left(-24\right)}{12}$$

Multiply 13 and -24 to get -312.

$$m=\frac{-312}{12}$$

Divide -312 by 12 to get -26.

$$m=-26$$