Solve z/5=3/10z+t

$$\frac { z } { 5 } = \frac { 3 } { 10 } z + t$$

Solve for t

$$t=-\frac{z}{10}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,10.

$$2z=3z+10t$$

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

$$3z+10t=2z$$

Subtract 3z from both sides.

$$10t=2z-3z$$

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

$$10t=-z$$

Divide both sides by 10.

$$\frac{10t}{10}=-\frac{z}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$t=-\frac{z}{10}$$

Solve for z

$$z=-10t$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,10.

$$2z=3z+10t$$

Subtract 3z from both sides.

$$2z-3z=10t$$

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

$$-z=10t$$

Divide both sides by -1.

$$\frac{-z}{-1}=\frac{10t}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$z=\frac{10t}{-1}$$

Divide 10t by -1.

$$z=-10t$$