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

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

Solve for v

$$v = -\frac{8}{5} = -1\frac{3}{5} = -1.6$$

Steps for Solving Linear Equation

Subtract \frac{2}{3}v from both sides.

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

Combine -\frac{7}{2}v and -\frac{2}{3}v to get -\frac{25}{6}v.

$$-\frac{25}{6}v-\frac{5}{3}=5$$

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

$$-\frac{25}{6}v=5+\frac{5}{3}$$

Convert 5 to fraction \frac{15}{3}.

$$-\frac{25}{6}v=\frac{15}{3}+\frac{5}{3}$$

Since \frac{15}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$-\frac{25}{6}v=\frac{15+5}{3}$$

Add 15 and 5 to get 20.

$$-\frac{25}{6}v=\frac{20}{3}$$

Multiply both sides by -\frac{6}{25}, the reciprocal of -\frac{25}{6}.

$$v=\frac{20}{3}\left(-\frac{6}{25}\right)$$

Multiply \frac{20}{3} times -\frac{6}{25} by multiplying numerator times numerator and denominator times denominator.

$$v=\frac{20\left(-6\right)}{3\times 25}$$

Do the multiplications in the fraction \frac{20\left(-6\right)}{3\times 25}.

$$v=\frac{-120}{75}$$

Reduce the fraction \frac{-120}{75} to lowest terms by extracting and canceling out 15.

$$v=-\frac{8}{5}$$