Algebra Examples

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

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 $- p x + 8 x$ .

Tap for more steps...

Step 3.1

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

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

Step 3.2

Factor $x$ out of $8 x$ .

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

Step 3.3

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.

Tap for more steps...

Step 4.1

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

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

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

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

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Simplify each term.

Tap for more steps...

Step 4.3.1.1

Move the negative in front of the fraction.

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

Step 4.3.1.2

Move the negative in front of the fraction.

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

Step 4.3.2

Simplify terms.

Tap for more steps...

Step 4.3.2.1

Combine the numerators over the common denominator.

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

Step 4.3.2.2

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

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

Step 4.3.2.3

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

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

Step 4.3.2.4

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

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

Step 4.3.2.5

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

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

Step 4.3.2.6

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

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

Step 4.3.2.7

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

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

Step 4.3.2.8

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

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

Step 4.3.2.9

Cancel the common factor.

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

Step 4.3.2.10

Rewrite the expression.

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