Solve for x -px+r=-8x-2

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

Step 1

Add $8 x$ to both sides of the equation.

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

Step 2

Subtract $r$ from both sides of the equation.

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

Step 3

Factor $x$ out of $- p x + 8 x$ .

Factor $x$ out of $- p x$ .

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

Factor $x$ out of $8 x$ .

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

Factor $x$ out of $x (- p) + x \cdot 8$ .

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

Step 4

Divide each term in $x (- p + 8) = - 2 - r$ by $- p + 8$ and simplify.

Divide each term in $x (- p + 8) = - 2 - r$ by $- p + 8$ .

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

Simplify the left side.

Cancel the common factor of $- p + 8$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

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

Simplify terms.

Combine the numerators over the common denominator.

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

Rewrite $- 2$ as $- 1 (2)$ .

$x = \frac{- 1 (2) - r}{- p + 8}$

Factor $- 1$ out of $- r$ .

$x = \frac{- 1 (2) - (r)}{- p + 8}$

Factor $- 1$ out of $- 1 (2) - (r)$ .

$x = \frac{- 1 (2 + r)}{- p + 8}$

Factor $- 1$ out of $- p$ .

$x = \frac{- 1 (2 + r)}{- (p) + 8}$

Rewrite $8$ as $- 1 (- 8)$ .

$x = \frac{- 1 (2 + r)}{- (p) - 1 (- 8)}$

Factor $- 1$ out of $- (p) - 1 (- 8)$ .

$x = \frac{- 1 (2 + r)}{- (p - 8)}$

Rewrite $- (p - 8)$ as $- 1 (p - 8)$ .

$x = \frac{- 1 (2 + r)}{- 1 (p - 8)}$

Cancel the common factor.

$x = \frac{- 1 (2 + r)}{- 1 (p - 8)}$

Rewrite the expression.

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

Solve for x -px+r=-8x-2

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