Solve t_{1}=v/g-1/2

$$t _ { 1 } = \frac { v } { g } - \frac { 1 } { 2 }$$

Solve for g

$$\left\{\begin{matrix}g=\frac{2v}{2t_{1}+1}\text{, }&v\neq 0\text{ and }t_{1}\neq -\frac{1}{2}\\g\neq 0\text{, }&t_{1}=-\frac{1}{2}\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$t_{1}\times 2g=2v+2g\left(-\frac{1}{2}\right)$$

Multiply 2 and -\frac{1}{2} to get -1.

$$t_{1}\times 2g=2v-g$$

Add g to both sides.

$$t_{1}\times 2g+g=2v$$

Combine all terms containing g.

$$\left(t_{1}\times 2+1\right)g=2v$$

The equation is in standard form.

$$\left(2t_{1}+1\right)g=2v$$

Divide both sides by 2t_{1}+1.

$$\frac{\left(2t_{1}+1\right)g}{2t_{1}+1}=\frac{2v}{2t_{1}+1}$$

Dividing by 2t_{1}+1 undoes the multiplication by 2t_{1}+1.

$$g=\frac{2v}{2t_{1}+1}$$

Variable g cannot be equal to 0.

$$g=\frac{2v}{2t_{1}+1}\text{, }g\neq 0$$

Solve for t_1

$$t_{1}=\frac{v}{g}-\frac{1}{2}$$

$$g\neq 0$$