Solve 2t=t-1/m-1

$$2 t = \frac { t - 1 } { m - 1 }$$

Solve for m

$$m=\frac{3}{2}-\frac{1}{2t}$$

$$t\neq 1\text{ and }t\neq 0$$

Steps for Solving Linear Equation

Variable m cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by m-1.

$$2t\left(m-1\right)=t-1$$

Use the distributive property to multiply 2t by m-1.

$$2tm-2t=t-1$$

Add 2t to both sides.

$$2tm=t-1+2t$$

Combine t and 2t to get 3t.

$$2tm=3t-1$$

Divide both sides by 2t.

$$\frac{2tm}{2t}=\frac{3t-1}{2t}$$

Dividing by 2t undoes the multiplication by 2t.

$$m=\frac{3t-1}{2t}$$

Divide 3t-1 by 2t.

$$m=\frac{3}{2}-\frac{1}{2t}$$

Variable m cannot be equal to 1.

$$m=\frac{3}{2}-\frac{1}{2t}\text{, }m\neq 1$$

Solve for t

$$t=-\frac{1}{2m-3}$$

$$m\neq \frac{3}{2}\text{ and }m\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by m-1.

$$2t\left(m-1\right)=t-1$$

Use the distributive property to multiply 2t by m-1.

$$2tm-2t=t-1$$

Subtract t from both sides.

$$2tm-2t-t=-1$$

Combine -2t and -t to get -3t.

$$2tm-3t=-1$$

Combine all terms containing t.

$$\left(2m-3\right)t=-1$$

Divide both sides by 2m-3.

$$\frac{\left(2m-3\right)t}{2m-3}=-\frac{1}{2m-3}$$

Dividing by 2m-3 undoes the multiplication by 2m-3.

$$t=-\frac{1}{2m-3}$$