Algebra Examples

$2 m - n x = x + 4$

Step 1

Subtract $x$ from both sides of the equation.

$2 m - n x - x = 4$

Step 2

Subtract $2 m$ from both sides of the equation.

$- n x - x = 4 - 2 m$

Step 3

Factor $x$ out of $- n x - x$ .

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Step 3.1

Factor $x$ out of $- n x$ .

$x (- n) - x = 4 - 2 m$

Step 3.2

Factor $x$ out of $- x$ .

$x (- n) + x \cdot - 1 = 4 - 2 m$

Step 3.3

Factor $x$ out of $x (- n) + x \cdot - 1$ .

$x (- n - 1) = 4 - 2 m$

Step 4

Divide each term in $x (- n - 1) = 4 - 2 m$ by $- n - 1$ and simplify.

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Step 4.1

Divide each term in $x (- n - 1) = 4 - 2 m$ by $- n - 1$ .

$\frac{x (- n - 1)}{- n - 1} = \frac{4}{- n - 1} + \frac{- 2 m}{- n - 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- n - 1$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x (- n - 1)}{- n - 1} = \frac{4}{- n - 1} + \frac{- 2 m}{- n - 1}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{- n - 1} + \frac{- 2 m}{- n - 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x = \frac{4}{- n - 1} - \frac{2 m}{- n - 1}$

Step 4.3.2

Combine the numerators over the common denominator.

$x = \frac{4 - 2 m}{- n - 1}$

Step 4.3.3

Factor $2$ out of $4 - 2 m$ .

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Step 4.3.3.1

Factor $2$ out of $4$ .

$x = \frac{2 (2) - 2 m}{- n - 1}$

Step 4.3.3.2

Factor $2$ out of $- 2 m$ .

$x = \frac{2 (2) + 2 (- m)}{- n - 1}$

Step 4.3.3.3

Factor $2$ out of $2 (2) + 2 (- m)$ .

$x = \frac{2 (2 - m)}{- n - 1}$

Step 4.3.4

Factor $- 1$ out of $- n$ .

$x = \frac{2 (2 - m)}{- (n) - 1}$

Step 4.3.5

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

$x = \frac{2 (2 - m)}{- (n) - 1 (1)}$

Step 4.3.6

Factor $- 1$ out of $- (n) - 1 (1)$ .

$x = \frac{2 (2 - m)}{- (n + 1)}$

Step 4.3.7

Rewrite negatives.

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Step 4.3.7.1

Rewrite $- (n + 1)$ as $- 1 (n + 1)$ .

$x = \frac{2 (2 - m)}{- 1 (n + 1)}$

Step 4.3.7.2

Move the negative in front of the fraction.

$x = - \frac{2 (2 - m)}{n + 1}$