Solve -1/2u-4/3=3/2

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

Solve for u

$$u = -\frac{17}{3} = -5\frac{2}{3} \approx -5.666666667$$

Steps for Solving Linear Equation

Add \frac{4}{3} to both sides.

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

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{4}{3} to fractions with denominator 6.

$$-\frac{1}{2}u=\frac{9}{6}+\frac{8}{6}$$

Since \frac{9}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}u=\frac{9+8}{6}$$

Add 9 and 8 to get 17.

$$-\frac{1}{2}u=\frac{17}{6}$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$u=\frac{17}{6}\left(-2\right)$$

Express \frac{17}{6}\left(-2\right) as a single fraction.

$$u=\frac{17\left(-2\right)}{6}$$

Multiply 17 and -2 to get -34.

$$u=\frac{-34}{6}$$

Reduce the fraction \frac{-34}{6} to lowest terms by extracting and canceling out 2.

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