Solve 1:5-1/v-15=1*5-1/30

$$\frac { 1 : 5 - 1 } { v - 15 } = \frac { 1 \cdot 5 - 1 } { 30 }$$

Solve for v

$$v=9$$

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 30\left(v-15\right), the least common multiple of v-15,30.

$$30\left(\frac{1}{5}-1\right)=\left(v-15\right)\left(1\times 5-1\right)$$

Subtract 1 from \frac{1}{5} to get -\frac{4}{5}.

$$30\left(-\frac{4}{5}\right)=\left(v-15\right)\left(1\times 5-1\right)$$

Multiply 30 and -\frac{4}{5} to get -24.

$$-24=\left(v-15\right)\left(1\times 5-1\right)$$

Multiply 1 and 5 to get 5.

$$-24=\left(v-15\right)\left(5-1\right)$$

Subtract 1 from 5 to get 4.

$$-24=\left(v-15\right)\times 4$$

Use the distributive property to multiply v-15 by 4.

$$-24=4v-60$$

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

$$4v-60=-24$$

Add 60 to both sides.

$$4v=-24+60$$

Add -24 and 60 to get 36.

$$4v=36$$

Divide both sides by 4.

$$v=\frac{36}{4}$$

Divide 36 by 4 to get 9.

$$v=9$$