Pre-Algebra Examples

$3 x + c = c x - 2$

Step 1

Subtract $c x$ from both sides of the equation.

$3 x + c - c x = - 2$

Step 2

Subtract $c$ from both sides of the equation.

$3 x - c x = - 2 - c$

Step 3

Factor $x$ out of $3 x - c x$ .

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Step 3.1

Factor $x$ out of $3 x$ .

$x \cdot 3 - c x = - 2 - c$

Step 3.2

Factor $x$ out of $- c x$ .

$x \cdot 3 + x (- c) = - 2 - c$

Step 3.3

Factor $x$ out of $x \cdot 3 + x (- c)$ .

$x (3 - c) = - 2 - c$

Step 4

Divide each term in $x (3 - c) = - 2 - c$ by $3 - c$ and simplify.

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Step 4.1

Divide each term in $x (3 - c) = - 2 - c$ by $3 - c$ .

$\frac{x (3 - c)}{3 - c} = \frac{- 2}{3 - c} + \frac{- c}{3 - c}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3 - c$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x (3 - c)}{3 - c} = \frac{- 2}{3 - c} + \frac{- c}{3 - c}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{3 - c} + \frac{- c}{3 - c}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$x = \frac{- 2 - c}{3 - c}$

Step 4.3.2

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

$x = \frac{- 1 (2) - c}{3 - c}$

Step 4.3.3

Factor $- 1$ out of $- c$ .

$x = \frac{- 1 (2) - (c)}{3 - c}$

Step 4.3.4

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

$x = \frac{- 1 (2 + c)}{3 - c}$

Step 4.3.5

Move the negative in front of the fraction.

$x = - \frac{2 + c}{3 - c}$