Solve -7/5=-1/2u-8/3

$$- \frac { 7 } { 5 } = - \frac { 1 } { 2 } u - \frac { 8 } { 3 }$$

Solve for u

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$-\frac{1}{2}u-\frac{8}{3}=-\frac{7}{5}$$

Add \frac{8}{3} to both sides.

$$-\frac{1}{2}u=-\frac{7}{5}+\frac{8}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{7}{5} and \frac{8}{3} to fractions with denominator 15.

$$-\frac{1}{2}u=-\frac{21}{15}+\frac{40}{15}$$

Since -\frac{21}{15} and \frac{40}{15} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}u=\frac{-21+40}{15}$$

Add -21 and 40 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.

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