Solve 1+2s/2-t=5s

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

Solve for s

$$s=-\frac{1}{5t-8}$$

$$t\neq \frac{8}{5}\text{ and }t\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -t+2.

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

Use the distributive property to multiply 5s by -t+2.

$$1+2s=-5st+10s$$

Add 5st to both sides.

$$1+2s+5st=10s$$

Subtract 10s from both sides.

$$1+2s+5st-10s=0$$

Combine 2s and -10s to get -8s.

$$1-8s+5st=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-8s+5st=-1$$

Combine all terms containing s.

$$\left(-8+5t\right)s=-1$$

The equation is in standard form.

$$\left(5t-8\right)s=-1$$

Divide both sides by 5t-8.

$$\frac{\left(5t-8\right)s}{5t-8}=-\frac{1}{5t-8}$$

Dividing by 5t-8 undoes the multiplication by 5t-8.

$$s=-\frac{1}{5t-8}$$

Solve for t

$$t=\frac{8}{5}-\frac{1}{5s}$$

$$s\neq -\frac{1}{2}\text{ and }s\neq 0$$

Steps for Solving Linear Equation

Variable t cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by -t+2.

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

Use the distributive property to multiply 5s by -t+2.

$$1+2s=-5st+10s$$

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

$$-5st+10s=1+2s$$

Subtract 10s from both sides.

$$-5st=1+2s-10s$$

Combine 2s and -10s to get -8s.

$$-5st=1-8s$$

The equation is in standard form.

$$\left(-5s\right)t=1-8s$$

Divide both sides by -5s.

$$\frac{\left(-5s\right)t}{-5s}=\frac{1-8s}{-5s}$$

Dividing by -5s undoes the multiplication by -5s.

$$t=\frac{1-8s}{-5s}$$

Divide 1-8s by -5s.

$$t=\frac{8}{5}-\frac{1}{5s}$$

Variable t cannot be equal to 2.

$$t=\frac{8}{5}-\frac{1}{5s}\text{, }t\neq 2$$