Solve 2x+1/t-3=-5

$$\frac { 2 x + 1 } { t - 3 } = - 5$$

Solve for t

$$t=\frac{14-2x}{5}$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Variable t cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by t-3.

$$2x+1=-5\left(t-3\right)$$

Use the distributive property to multiply -5 by t-3.

$$2x+1=-5t+15$$

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

$$-5t+15=2x+1$$

Subtract 15 from both sides.

$$-5t=2x+1-15$$

Subtract 15 from 1 to get -14.

$$-5t=2x-14$$

Divide both sides by -5.

$$\frac{-5t}{-5}=\frac{2x-14}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$t=\frac{2x-14}{-5}$$

Divide -14+2x by -5.

$$t=\frac{14-2x}{5}$$

Variable t cannot be equal to 3.

$$t=\frac{14-2x}{5}\text{, }t\neq 3$$

Solve for x

$$x=-\frac{5t}{2}+7$$

$$t\neq 3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by t-3.

$$2x+1=-5\left(t-3\right)$$

Use the distributive property to multiply -5 by t-3.

$$2x+1=-5t+15$$

Subtract 1 from both sides.

$$2x=-5t+15-1$$

Subtract 1 from 15 to get 14.

$$2x=-5t+14$$

The equation is in standard form.

$$2x=14-5t$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{14-5t}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{14-5t}{2}$$

Divide -5t+14 by 2.

$$x=-\frac{5t}{2}+7$$