Solve -2v-5/3=7/2v-1/2

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

Solve for v

$$v=-\frac{7}{33}\approx -0.212121212$$

Steps for Solving Linear Equation

Subtract \frac{7}{2}v from both sides.

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

Combine -2v and -\frac{7}{2}v to get -\frac{11}{2}v.

$$-\frac{11}{2}v-\frac{5}{3}=-\frac{1}{2}$$

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

$$-\frac{11}{2}v=-\frac{1}{2}+\frac{5}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{5}{3} to fractions with denominator 6.

$$-\frac{11}{2}v=-\frac{3}{6}+\frac{10}{6}$$

Since -\frac{3}{6} and \frac{10}{6} have the same denominator, add them by adding their numerators.

$$-\frac{11}{2}v=\frac{-3+10}{6}$$

Add -3 and 10 to get 7.

$$-\frac{11}{2}v=\frac{7}{6}$$

Multiply both sides by -\frac{2}{11}, the reciprocal of -\frac{11}{2}.

$$v=\frac{7}{6}\left(-\frac{2}{11}\right)$$

Multiply \frac{7}{6} times -\frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$v=\frac{7\left(-2\right)}{6\times 11}$$

Do the multiplications in the fraction \frac{7\left(-2\right)}{6\times 11}.

$$v=\frac{-14}{66}$$

Reduce the fraction \frac{-14}{66} to lowest terms by extracting and canceling out 2.

$$v=-\frac{7}{33}$$