Solve 1/3-1/2m=1/6m+7/9

$$\frac{ 1 }{ 3 } - \frac{ 1 }{ 2 } m = \frac{ 1 }{ 6 } m+ \frac{ 7 }{ 9 }$$

Solve for m

$$m=-\frac{2}{3}\approx -0.666666667$$

Steps for Solving Linear Equation

Subtract \frac{1}{6}m from both sides.

$$\frac{1}{3}-\frac{1}{2}m-\frac{1}{6}m=\frac{7}{9}$$

Combine -\frac{1}{2}m and -\frac{1}{6}m to get -\frac{2}{3}m.

$$\frac{1}{3}-\frac{2}{3}m=\frac{7}{9}$$

Subtract \frac{1}{3} from both sides.

$$-\frac{2}{3}m=\frac{7}{9}-\frac{1}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{7}{9} and \frac{1}{3} to fractions with denominator 9.

$$-\frac{2}{3}m=\frac{7}{9}-\frac{3}{9}$$

Since \frac{7}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{3}m=\frac{7-3}{9}$$

Subtract 3 from 7 to get 4.

$$-\frac{2}{3}m=\frac{4}{9}$$

Multiply both sides by -\frac{3}{2}, the reciprocal of -\frac{2}{3}.

$$m=\frac{4}{9}\left(-\frac{3}{2}\right)$$

Multiply \frac{4}{9} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$m=\frac{4\left(-3\right)}{9\times 2}$$

Do the multiplications in the fraction \frac{4\left(-3\right)}{9\times 2}.

$$m=\frac{-12}{18}$$

Reduce the fraction \frac{-12}{18} to lowest terms by extracting and canceling out 6.

$$m=-\frac{2}{3}$$