Solve t+1/v=5/2

$$t + \frac { 1 } { v } = \frac { 5 } { 2 }$$

Solve for t

$$t=\frac{5}{2}-\frac{1}{v}$$

$$v\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2v, the least common multiple of v,2.

$$2vt+2=5v$$

Subtract 2 from both sides.

$$2vt=5v-2$$

Divide both sides by 2v.

$$\frac{2vt}{2v}=\frac{5v-2}{2v}$$

Dividing by 2v undoes the multiplication by 2v.

$$t=\frac{5v-2}{2v}$$

Divide 5v-2 by 2v.

$$t=\frac{5}{2}-\frac{1}{v}$$

Solve for v

$$v=-\frac{2}{2t-5}$$

$$t\neq \frac{5}{2}$$

Steps for Solving Linear Equation

Variable v cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2v, the least common multiple of v,2.

$$2vt+2=5v$$

Subtract 5v from both sides.

$$2vt+2-5v=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$2vt-5v=-2$$

Combine all terms containing v.

$$\left(2t-5\right)v=-2$$

Divide both sides by 2t-5.

$$\frac{\left(2t-5\right)v}{2t-5}=-\frac{2}{2t-5}$$

Dividing by 2t-5 undoes the multiplication by 2t-5.

$$v=-\frac{2}{2t-5}$$

Variable v cannot be equal to 0.

$$v=-\frac{2}{2t-5}\text{, }v\neq 0$$