Solve 1/3-6/7w=-1/2

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

Solve for w

$$w=\frac{35}{36}\approx 0.972222222$$

Steps for Solving Linear Equation

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

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

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

$$-\frac{6}{7}w=-\frac{3}{6}-\frac{2}{6}$$

Since -\frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{6}{7}w=\frac{-3-2}{6}$$

Subtract 2 from -3 to get -5.

$$-\frac{6}{7}w=-\frac{5}{6}$$

Multiply both sides by -\frac{7}{6}, the reciprocal of -\frac{6}{7}.

$$w=-\frac{5}{6}\left(-\frac{7}{6}\right)$$

Multiply -\frac{5}{6} times -\frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{-5\left(-7\right)}{6\times 6}$$

Do the multiplications in the fraction \frac{-5\left(-7\right)}{6\times 6}.

$$w=\frac{35}{36}$$