Solve v+3/4-y-3/2-y+7/6=3+y/-8

$$\frac { v + 3 } { 4 } - \frac { y - 3 } { 2 } - \frac { y + 7 } { 6 } = \frac { 3 + y } { - 8 }$$

Solve for v

$$v=\frac{13y-35}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 4,2,6,-8.

$$6\left(v+3\right)-12\left(y-3\right)-4\left(y+7\right)=-3\left(3+y\right)$$

Use the distributive property to multiply 6 by v+3.

$$6v+18-12\left(y-3\right)-4\left(y+7\right)=-3\left(3+y\right)$$

Use the distributive property to multiply -12 by y-3.

$$6v+18-12y+36-4\left(y+7\right)=-3\left(3+y\right)$$

Add 18 and 36 to get 54.

$$6v+54-12y-4\left(y+7\right)=-3\left(3+y\right)$$

Use the distributive property to multiply -4 by y+7.

$$6v+54-12y-4y-28=-3\left(3+y\right)$$

Combine -12y and -4y to get -16y.

$$6v+54-16y-28=-3\left(3+y\right)$$

Subtract 28 from 54 to get 26.

$$6v+26-16y=-3\left(3+y\right)$$

Use the distributive property to multiply -3 by 3+y.

$$6v+26-16y=-9-3y$$

Subtract 26 from both sides.

$$6v-16y=-9-3y-26$$

Subtract 26 from -9 to get -35.

$$6v-16y=-35-3y$$

Add 16y to both sides.

$$6v=-35-3y+16y$$

Combine -3y and 16y to get 13y.

$$6v=-35+13y$$

The equation is in standard form.

$$6v=13y-35$$

Divide both sides by 6.

$$\frac{6v}{6}=\frac{13y-35}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$v=\frac{13y-35}{6}$$

Solve for y

$$y=\frac{6v+35}{13}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 4,2,6,-8.

$$6\left(v+3\right)-12\left(y-3\right)-4\left(y+7\right)=-3\left(3+y\right)$$

Use the distributive property to multiply 6 by v+3.

$$6v+18-12\left(y-3\right)-4\left(y+7\right)=-3\left(3+y\right)$$

Use the distributive property to multiply -12 by y-3.

$$6v+18-12y+36-4\left(y+7\right)=-3\left(3+y\right)$$

Add 18 and 36 to get 54.

$$6v+54-12y-4\left(y+7\right)=-3\left(3+y\right)$$

Use the distributive property to multiply -4 by y+7.

$$6v+54-12y-4y-28=-3\left(3+y\right)$$

Combine -12y and -4y to get -16y.

$$6v+54-16y-28=-3\left(3+y\right)$$

Subtract 28 from 54 to get 26.

$$6v+26-16y=-3\left(3+y\right)$$

Use the distributive property to multiply -3 by 3+y.

$$6v+26-16y=-9-3y$$

Add 3y to both sides.

$$6v+26-16y+3y=-9$$

Combine -16y and 3y to get -13y.

$$6v+26-13y=-9$$

Subtract 6v from both sides.

$$26-13y=-9-6v$$

Subtract 26 from both sides.

$$-13y=-9-6v-26$$

Subtract 26 from -9 to get -35.

$$-13y=-35-6v$$

The equation is in standard form.

$$-13y=-6v-35$$

Divide both sides by -13.

$$\frac{-13y}{-13}=\frac{-6v-35}{-13}$$

Dividing by -13 undoes the multiplication by -13.

$$y=\frac{-6v-35}{-13}$$

Divide -35-6v by -13.

$$y=\frac{6v+35}{13}$$