Solve -3/2v-5/4v=-5/6+3/5

$$- \frac { 3 } { 2 } v - \frac { 5 } { 4 } v = \frac { - 5 } { 6 } + \frac { 3 } { 5 }$$

Solve for v

$$v=\frac{14}{165}\approx 0.084848485$$

Steps for Solving Linear Equation

Combine -\frac{3}{2}v and -\frac{5}{4}v to get -\frac{11}{4}v.

$$-\frac{11}{4}v=\frac{-5}{6}+\frac{3}{5}$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$-\frac{11}{4}v=-\frac{5}{6}+\frac{3}{5}$$

Least common multiple of 6 and 5 is 30. Convert -\frac{5}{6} and \frac{3}{5} to fractions with denominator 30.

$$-\frac{11}{4}v=-\frac{25}{30}+\frac{18}{30}$$

Since -\frac{25}{30} and \frac{18}{30} have the same denominator, add them by adding their numerators.

$$-\frac{11}{4}v=\frac{-25+18}{30}$$

Add -25 and 18 to get -7.

$$-\frac{11}{4}v=-\frac{7}{30}$$

Multiply both sides by -\frac{4}{11}, the reciprocal of -\frac{11}{4}.

$$v=-\frac{7}{30}\left(-\frac{4}{11}\right)$$

Multiply -\frac{7}{30} times -\frac{4}{11} by multiplying numerator times numerator and denominator times denominator.

$$v=\frac{-7\left(-4\right)}{30\times 11}$$

Do the multiplications in the fraction \frac{-7\left(-4\right)}{30\times 11}.

$$v=\frac{28}{330}$$

Reduce the fraction \frac{28}{330} to lowest terms by extracting and canceling out 2.

$$v=\frac{14}{165}$$