Solve 10v-10v_{s}=5v+5v_{s}

$$10 v - 10 v _ { s } = 5 v + 5 v _ { s }$$

Solve for v

$$v=3v_{s}$$

Steps for Solving Linear Equation

Subtract 5v from both sides.

$$10v-10v_{s}-5v=5v_{s}$$

Combine 10v and -5v to get 5v.

$$5v-10v_{s}=5v_{s}$$

Add 10v_{s} to both sides.

$$5v=5v_{s}+10v_{s}$$

Combine 5v_{s} and 10v_{s} to get 15v_{s}.

$$5v=15v_{s}$$

Divide both sides by 5.

$$\frac{5v}{5}=\frac{15v_{s}}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$v=\frac{15v_{s}}{5}$$

Divide 15v_{s} by 5.

$$v=3v_{s}$$

Solve for v_s

$$v_{s}=\frac{v}{3}$$

Steps for Solving Linear Equation

Subtract 5v_{s} from both sides.

$$10v-10v_{s}-5v_{s}=5v$$

Combine -10v_{s} and -5v_{s} to get -15v_{s}.

$$10v-15v_{s}=5v$$

Subtract 10v from both sides.

$$-15v_{s}=5v-10v$$

Combine 5v and -10v to get -5v.

$$-15v_{s}=-5v$$

Divide both sides by -15.

$$\frac{-15v_{s}}{-15}=-\frac{5v}{-15}$$

Dividing by -15 undoes the multiplication by -15.

$$v_{s}=-\frac{5v}{-15}$$

Divide -5v by -15.

$$v_{s}=\frac{v}{3}$$