Solve (-8/9)*n+5/6=7/8

$$( - \frac { 8 } { 9 } ) \cdot n + \frac { 5 } { 6 } = \frac { 7 } { 8 }$$

Solve for n

$$n=-\frac{3}{64}=-0.046875$$

Steps for Solving Linear Equation

Subtract \frac{5}{6} from both sides.

$$-\frac{8}{9}n=\frac{7}{8}-\frac{5}{6}$$

Least common multiple of 8 and 6 is 24. Convert \frac{7}{8} and \frac{5}{6} to fractions with denominator 24.

$$-\frac{8}{9}n=\frac{21}{24}-\frac{20}{24}$$

Since \frac{21}{24} and \frac{20}{24} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{8}{9}n=\frac{21-20}{24}$$

Subtract 20 from 21 to get 1.

$$-\frac{8}{9}n=\frac{1}{24}$$

Multiply both sides by -\frac{9}{8}, the reciprocal of -\frac{8}{9}.

$$n=\frac{1}{24}\left(-\frac{9}{8}\right)$$

Multiply \frac{1}{24} times -\frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$n=\frac{1\left(-9\right)}{24\times 8}$$

Do the multiplications in the fraction \frac{1\left(-9\right)}{24\times 8}.

$$n=\frac{-9}{192}$$

Reduce the fraction \frac{-9}{192} to lowest terms by extracting and canceling out 3.

$$n=-\frac{3}{64}$$