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

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

Solve for u

$$u = -\frac{38}{15} = -2\frac{8}{15} \approx -2.533333333$$

Steps for Solving Linear Equation

Add \frac{3}{5} to both sides.

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

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{3}{5} to fractions with denominator 15.

$$-\frac{1}{2}u=\frac{10}{15}+\frac{9}{15}$$

Since \frac{10}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}u=\frac{10+9}{15}$$

Add 10 and 9 to get 19.

$$-\frac{1}{2}u=\frac{19}{15}$$

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

$$u=\frac{19}{15}\left(-2\right)$$

Express \frac{19}{15}\left(-2\right) as a single fraction.

$$u=\frac{19\left(-2\right)}{15}$$

Multiply 19 and -2 to get -38.

$$u=\frac{-38}{15}$$

Fraction \frac{-38}{15} can be rewritten as -\frac{38}{15} by extracting the negative sign.

$$u=-\frac{38}{15}$$