Solve 8y/v-4=32/v-4-3

$$\frac { 8 y } { v - 4 } = \frac { 32 } { v - 4 } - 3$$

Solve for v

$$v=\frac{44-8y}{3}$$

$$y\neq 4$$

Steps for Solving Linear Equation

Variable v cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by v-4.

$$8y=32+\left(v-4\right)\left(-3\right)$$

Use the distributive property to multiply v-4 by -3.

$$8y=32-3v+12$$

Add 32 and 12 to get 44.

$$8y=44-3v$$

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

$$44-3v=8y$$

Subtract 44 from both sides.

$$-3v=8y-44$$

Divide both sides by -3.

$$\frac{-3v}{-3}=\frac{8y-44}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$v=\frac{8y-44}{-3}$$

Divide 8y-44 by -3.

$$v=\frac{44-8y}{3}$$

Variable v cannot be equal to 4.

$$v=\frac{44-8y}{3}\text{, }v\neq 4$$

Solve for y

$$y=-\frac{3v}{8}+\frac{11}{2}$$

$$v\neq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by v-4.

$$8y=32+\left(v-4\right)\left(-3\right)$$

Use the distributive property to multiply v-4 by -3.

$$8y=32-3v+12$$

Add 32 and 12 to get 44.

$$8y=44-3v$$

Divide both sides by 8.

$$\frac{8y}{8}=\frac{44-3v}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$y=\frac{44-3v}{8}$$

Divide 44-3v by 8.

$$y=-\frac{3v}{8}+\frac{11}{2}$$