Solve -6u+1/2=-6/5u-3/5

$$- 6 u + \frac { 1 } { 2 } = - \frac { 6 } { 5 } u - \frac { 3 } { 5 }$$

Solve for u

$$u=\frac{11}{48}\approx 0.229166667$$

Steps for Solving Linear Equation

Add \frac{6}{5}u to both sides.

$$-6u+\frac{1}{2}+\frac{6}{5}u=-\frac{3}{5}$$

Combine -6u and \frac{6}{5}u to get -\frac{24}{5}u.

$$-\frac{24}{5}u+\frac{1}{2}=-\frac{3}{5}$$

Subtract \frac{1}{2} from both sides.

$$-\frac{24}{5}u=-\frac{3}{5}-\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert -\frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$-\frac{24}{5}u=-\frac{6}{10}-\frac{5}{10}$$

Since -\frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{24}{5}u=\frac{-6-5}{10}$$

Subtract 5 from -6 to get -11.

$$-\frac{24}{5}u=-\frac{11}{10}$$

Multiply both sides by -\frac{5}{24}, the reciprocal of -\frac{24}{5}.

$$u=-\frac{11}{10}\left(-\frac{5}{24}\right)$$

Multiply -\frac{11}{10} times -\frac{5}{24} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{-11\left(-5\right)}{10\times 24}$$

Do the multiplications in the fraction \frac{-11\left(-5\right)}{10\times 24}.

$$u=\frac{55}{240}$$

Reduce the fraction \frac{55}{240} to lowest terms by extracting and canceling out 5.

$$u=\frac{11}{48}$$