Solve sv-s=7w-c

$$s v - s = 7 w - c$$

Solve for s (complex solution)

$$\left\{\begin{matrix}s=-\frac{c-7w}{v-1}\text{, }&v\neq 1\\s\in \mathrm{C}\text{, }&w=\frac{c}{7}\text{ and }v=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing s.

$$\left(v-1\right)s=7w-c$$

Divide both sides by v-1.

$$\frac{\left(v-1\right)s}{v-1}=\frac{7w-c}{v-1}$$

Dividing by v-1 undoes the multiplication by v-1.

$$s=\frac{7w-c}{v-1}$$

Solve for c

$$c=7w+s-sv$$

Steps for Solving Linear Equation

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

$$7w-c=sv-s$$

Subtract 7w from both sides.

$$-c=sv-s-7w$$

Divide both sides by -1.

$$\frac{-c}{-1}=\frac{sv-s-7w}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$c=\frac{sv-s-7w}{-1}$$

Divide sv-s-7w by -1.

$$c=7w+s-sv$$

Solve for s

$$\left\{\begin{matrix}s=-\frac{c-7w}{v-1}\text{, }&v\neq 1\\s\in \mathrm{R}\text{, }&w=\frac{c}{7}\text{ and }v=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing s.

$$\left(v-1\right)s=7w-c$$

Divide both sides by v-1.

$$\frac{\left(v-1\right)s}{v-1}=\frac{7w-c}{v-1}$$

Dividing by v-1 undoes the multiplication by v-1.

$$s=\frac{7w-c}{v-1}$$