Solve -u+4/5=-1/3u-1/3

$$- u + \frac { 4 } { 5 } = - \frac { 1 } { 3 } u - \frac { 1 } { 3 }$$

Solve for u

$$u = \frac{17}{10} = 1\frac{7}{10} = 1.7$$

Steps for Solving Linear Equation

Add \frac{1}{3}u to both sides.

$$-u+\frac{4}{5}+\frac{1}{3}u=-\frac{1}{3}$$

Subtract \frac{4}{5} from both sides.

$$-u+\frac{1}{3}u=-\frac{1}{3}-\frac{4}{5}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{1}{3} and \frac{4}{5} to fractions with denominator 15.

$$-u+\frac{1}{3}u=-\frac{5}{15}-\frac{12}{15}$$

Since -\frac{5}{15} and \frac{12}{15} have the same denominator, subtract them by subtracting their numerators.

$$-u+\frac{1}{3}u=\frac{-5-12}{15}$$

Subtract 12 from -5 to get -17.

$$-u+\frac{1}{3}u=-\frac{17}{15}$$

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

$$-\frac{2}{3}u=-\frac{17}{15}$$

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

$$u=-\frac{17}{15}\left(-\frac{3}{2}\right)$$

Multiply -\frac{17}{15} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{-17\left(-3\right)}{15\times 2}$$

Do the multiplications in the fraction \frac{-17\left(-3\right)}{15\times 2}.

$$u=\frac{51}{30}$$

Reduce the fraction \frac{51}{30} to lowest terms by extracting and canceling out 3.

$$u=\frac{17}{10}$$