Solve 30/15+v=9/2-30/15-6

$$\frac { 30 } { 15 + v } = \frac { 9 } { 2 } - \frac { 30 } { 15 - 6 }$$

Solve for v

$$v = \frac{75}{7} = 10\frac{5}{7} \approx 10.714285714$$

Steps for Solving Linear Equation

Variable v cannot be equal to -15 since division by zero is not defined. Multiply both sides of the equation by 2\left(v+15\right), the least common multiple of 15+v,2.

$$2\times 30=2\left(v+15\right)\times \frac{9}{2}-\left(\frac{2}{9}v+\frac{10}{3}\right)\times 30$$

Multiply 2 and 30 to get 60.

$$60=2\left(v+15\right)\times \frac{9}{2}-\left(\frac{2}{9}v+\frac{10}{3}\right)\times 30$$

Multiply 2 and \frac{9}{2} to get 9.

$$60=9\left(v+15\right)-\left(\frac{2}{9}v+\frac{10}{3}\right)\times 30$$

Use the distributive property to multiply 9 by v+15.

$$60=9v+135-\left(\frac{2}{9}v+\frac{10}{3}\right)\times 30$$

Use the distributive property to multiply \frac{2}{9}v+\frac{10}{3} by 30.

$$60=9v+135-\left(\frac{20}{3}v+100\right)$$

To find the opposite of \frac{20}{3}v+100, find the opposite of each term.

$$60=9v+135-\frac{20}{3}v-100$$

Combine 9v and -\frac{20}{3}v to get \frac{7}{3}v.

$$60=\frac{7}{3}v+135-100$$

Subtract 100 from 135 to get 35.

$$60=\frac{7}{3}v+35$$

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

$$\frac{7}{3}v+35=60$$

Subtract 35 from both sides.

$$\frac{7}{3}v=60-35$$

Subtract 35 from 60 to get 25.

$$\frac{7}{3}v=25$$

Multiply both sides by \frac{3}{7}, the reciprocal of \frac{7}{3}.

$$v=25\times \frac{3}{7}$$

Multiply 25 and \frac{3}{7} to get \frac{75}{7}.

$$v=\frac{75}{7}$$