Solve n-7/4=-35/12+5/3n

$$n - \frac { 7 } { 4 } = - \frac { 35 } { 12 } + \frac { 5 } { 3 } n$$

Solve for n

$$n = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps for Solving Linear Equation

Subtract \frac{5}{3}n from both sides.

$$n-\frac{7}{4}-\frac{5}{3}n=-\frac{35}{12}$$

Combine n and -\frac{5}{3}n to get -\frac{2}{3}n.

$$-\frac{2}{3}n-\frac{7}{4}=-\frac{35}{12}$$

Add \frac{7}{4} to both sides.

$$-\frac{2}{3}n=-\frac{35}{12}+\frac{7}{4}$$

Least common multiple of 12 and 4 is 12. Convert -\frac{35}{12} and \frac{7}{4} to fractions with denominator 12.

$$-\frac{2}{3}n=-\frac{35}{12}+\frac{21}{12}$$

Since -\frac{35}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}n=\frac{-35+21}{12}$$

Add -35 and 21 to get -14.

$$-\frac{2}{3}n=\frac{-14}{12}$$

Reduce the fraction \frac{-14}{12} to lowest terms by extracting and canceling out 2.

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

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

$$n=-\frac{7}{6}\left(-\frac{3}{2}\right)$$

Multiply -\frac{7}{6} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$n=\frac{-7\left(-3\right)}{6\times 2}$$

Do the multiplications in the fraction \frac{-7\left(-3\right)}{6\times 2}.

$$n=\frac{21}{12}$$

Reduce the fraction \frac{21}{12} to lowest terms by extracting and canceling out 3.

$$n=\frac{7}{4}$$