Algebra Examples

$c (x + 2) - 5 = b (x - 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$c x + c \cdot 2 - 5 = b (x - 3)$

Step 1.2

Move $2$ to the left of $c$ .

$c x + 2 c - 5 = b (x - 3)$

Step 2

Simplify $b (x - 3)$ .

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Step 2.1

Apply the distributive property.

$c x + 2 c - 5 = b x + b \cdot - 3$

Step 2.2

Move $- 3$ to the left of $b$ .

$c x + 2 c - 5 = b x - 3 b$

Step 3

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

$c x + 2 c - 5 - b x = - 3 b$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

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

$c x - 5 - b x = - 3 b - 2 c$

Step 4.2

Add $5$ to both sides of the equation.

$c x - b x = - 3 b - 2 c + 5$

Step 5

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

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Step 5.1

Factor $x$ out of $c x$ .

$x c - b x = - 3 b - 2 c + 5$

Step 5.2

Factor $x$ out of $- b x$ .

$x c + x (- b) = - 3 b - 2 c + 5$

Step 5.3

Factor $x$ out of $x c + x (- b)$ .

$x (c - b) = - 3 b - 2 c + 5$

Step 6

Divide each term in $x (c - b) = - 3 b - 2 c + 5$ by $c - b$ and simplify.

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Step 6.1

Divide each term in $x (c - b) = - 3 b - 2 c + 5$ by $c - b$ .

$\frac{x (c - b)}{c - b} = \frac{- 3 b}{c - b} + \frac{- 2 c}{c - b} + \frac{5}{c - b}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $c - b$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{x (c - b)}{c - b} = \frac{- 3 b}{c - b} + \frac{- 2 c}{c - b} + \frac{5}{c - b}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3 b}{c - b} + \frac{- 2 c}{c - b} + \frac{5}{c - b}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Simplify each term.

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Step 6.3.1.1

Move the negative in front of the fraction.

$x = - \frac{3 b}{c - b} + \frac{- 2 c}{c - b} + \frac{5}{c - b}$

Step 6.3.1.2

Move the negative in front of the fraction.

$x = - \frac{3 b}{c - b} - \frac{2 c}{c - b} + \frac{5}{c - b}$

Step 6.3.2

Simplify terms.

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Step 6.3.2.1

Combine the numerators over the common denominator.

$x = \frac{- 3 b - 2 c}{c - b} + \frac{5}{c - b}$

Step 6.3.2.2

Combine the numerators over the common denominator.

$x = \frac{- 3 b - 2 c + 5}{c - b}$

Step 6.3.2.3

Factor $- 1$ out of $- 3 b$ .

$x = \frac{- (3 b) - 2 c + 5}{c - b}$

Step 6.3.2.4

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

$x = \frac{- (3 b) - (2 c) + 5}{c - b}$

Step 6.3.2.5

Factor $- 1$ out of $- (3 b) - (2 c)$ .

$x = \frac{- (3 b + 2 c) + 5}{c - b}$

Step 6.3.2.6

Rewrite $5$ as $- 1 (- 5)$ .

$x = \frac{- (3 b + 2 c) - 1 (- 5)}{c - b}$

Step 6.3.2.7

Factor $- 1$ out of $- (3 b + 2 c) - 1 (- 5)$ .

$x = \frac{- (3 b + 2 c - 5)}{c - b}$

Step 6.3.2.8

Simplify the expression.

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Step 6.3.2.8.1

Rewrite $- (3 b + 2 c - 5)$ as $- 1 (3 b + 2 c - 5)$ .

$x = \frac{- 1 (3 b + 2 c - 5)}{c - b}$

Step 6.3.2.8.2

Move the negative in front of the fraction.

$x = - \frac{3 b + 2 c - 5}{c - b}$