Solve -7u+1/3=-5/4u-1/2

$$- 7 u + \frac { 1 } { 3 } = - \frac { 5 } { 4 } u - \frac { 1 } { 2 }$$

Solve for u

$$u=\frac{10}{69}\approx 0.144927536$$

Steps for Solving Linear Equation

Add \frac{5}{4}u to both sides.

$$-7u+\frac{1}{3}+\frac{5}{4}u=-\frac{1}{2}$$

Combine -7u and \frac{5}{4}u to get -\frac{23}{4}u.

$$-\frac{23}{4}u+\frac{1}{3}=-\frac{1}{2}$$

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

$$-\frac{23}{4}u=-\frac{1}{2}-\frac{1}{3}$$

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

$$-\frac{23}{4}u=-\frac{3}{6}-\frac{2}{6}$$

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

$$-\frac{23}{4}u=\frac{-3-2}{6}$$

Subtract 2 from -3 to get -5.

$$-\frac{23}{4}u=-\frac{5}{6}$$

Multiply both sides by -\frac{4}{23}, the reciprocal of -\frac{23}{4}.

$$u=-\frac{5}{6}\left(-\frac{4}{23}\right)$$

Multiply -\frac{5}{6} times -\frac{4}{23} by multiplying numerator times numerator and denominator times denominator.

$$u=\frac{-5\left(-4\right)}{6\times 23}$$

Do the multiplications in the fraction \frac{-5\left(-4\right)}{6\times 23}.

$$u=\frac{20}{138}$$

Reduce the fraction \frac{20}{138} to lowest terms by extracting and canceling out 2.

$$u=\frac{10}{69}$$