Solve -px+8x=-2-r

$$- p x + 8 x = - 2 - r$$

Solve for p

$$\left\{\begin{matrix}p=\frac{8x+r+2}{x}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&x=0\text{ and }r=-2\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 8x from both sides.

$$\left(-p\right)x=-2-r-8x$$

Reorder the terms.

$$-px=-8x-r-2$$

The equation is in standard form.

$$\left(-x\right)p=-8x-r-2$$

Divide both sides by -x.

$$\frac{\left(-x\right)p}{-x}=\frac{-8x-r-2}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$p=\frac{-8x-r-2}{-x}$$

Divide -8x-r-2 by -x.

$$p=\frac{r+2}{x}+8$$

Solve for r

$$r=px-8x-2$$

Steps for Solving Linear Equation

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

$$-2-r=\left(-p\right)x+8x$$

Add 2 to both sides.

$$-r=\left(-p\right)x+8x+2$$

Reorder the terms.

$$-r=-px+8x+2$$

The equation is in standard form.

$$-r=2+8x-px$$

Divide both sides by -1.

$$\frac{-r}{-1}=\frac{2+8x-px}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$r=\frac{2+8x-px}{-1}$$

Divide -px+8x+2 by -1.

$$r=px-8x-2$$