Solve 12-v/18=v-3/6+v+6/9+v/3

$$\frac { 12 - v } { 18 } = \frac { v - 3 } { 6 } + \frac { v + 6 } { 9 } + \frac { v } { 3 }$$

Solve for v

$$v=\frac{3}{4}=0.75$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 18,6,9,3.

$$12-v=3\left(v-3\right)+2\left(v+6\right)+6v$$

Use the distributive property to multiply 3 by v-3.

$$12-v=3v-9+2\left(v+6\right)+6v$$

Use the distributive property to multiply 2 by v+6.

$$12-v=3v-9+2v+12+6v$$

Combine 3v and 2v to get 5v.

$$12-v=5v-9+12+6v$$

Add -9 and 12 to get 3.

$$12-v=5v+3+6v$$

Combine 5v and 6v to get 11v.

$$12-v=11v+3$$

Subtract 11v from both sides.

$$12-v-11v=3$$

Combine -v and -11v to get -12v.

$$12-12v=3$$

Subtract 12 from both sides.

$$-12v=3-12$$

Subtract 12 from 3 to get -9.

$$-12v=-9$$

Divide both sides by -12.

$$v=\frac{-9}{-12}$$

Reduce the fraction \frac{-9}{-12} to lowest terms by extracting and canceling out -3.

$$v=\frac{3}{4}$$