Finite Math Examples

$a = b (1 - c) - d$

Step 1

Rewrite the equation as $b (1 - c) - d = a$ .

$b (1 - c) - d = a$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$b \cdot 1 + b (- c) - d = a$

Step 2.2

Multiply $b$ by $1$ .

$b + b (- c) - d = a$

Step 2.3

Rewrite using the commutative property of multiplication.

$b - b c - d = a$

Step 3

Add $d$ to both sides of the equation.

$b - b c = a + d$

Step 4

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

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Step 4.1

Factor $b$ out of $b^{1}$ .

$b \cdot 1 - b c = a + d$

Step 4.2

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

$b \cdot 1 + b (- 1 c) = a + d$

Step 4.3

Factor $b$ out of $b \cdot 1 + b (- 1 c)$ .

$b (1 - 1 c) = a + d$

Step 5

Rewrite $- 1 c$ as $- c$ .

$b (1 - c) = a + d$

Step 6

Divide each term in $b (1 - c) = a + d$ by $1 - c$ and simplify.

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Step 6.1

Divide each term in $b (1 - c) = a + d$ by $1 - c$ .

$\frac{b (1 - c)}{1 - c} = \frac{a}{1 - c} + \frac{d}{1 - c}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $1 - c$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{b (1 - c)}{1 - c} = \frac{a}{1 - c} + \frac{d}{1 - c}$

Step 6.2.1.2

Divide $b$ by $1$ .

$b = \frac{a}{1 - c} + \frac{d}{1 - c}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Combine the numerators over the common denominator.

$b = \frac{a + d}{1 - c}$