Finite Math Examples

$10 ((\frac{20 (b + 220)}{b - 20}) - 2 \cdot 10) (b - 2 \cdot 10) = 48000$

Step 1

Subtract $48000$ from both sides of the equation.

$10 ((\frac{20 (b + 220)}{b - 20}) - 2 \cdot 10) (b - 2 \cdot 10) - 48000 = 0$

Step 2

Simplify $10 ((\frac{20 (b + 220)}{b - 20}) - 2 \cdot 10) (b - 2 \cdot 10) - 48000$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- 2$ by $10$ .

$10 (\frac{20 (b + 220)}{b - 20} - 20) (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.2

To write $- 20$ as a fraction with a common denominator, multiply by $\frac{b - 20}{b - 20}$ .

$10 (\frac{20 (b + 220)}{b - 20} - 20 \cdot \frac{b - 20}{b - 20}) (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.3

Combine $- 20$ and $\frac{b - 20}{b - 20}$ .

$10 (\frac{20 (b + 220)}{b - 20} + \frac{- 20 (b - 20)}{b - 20}) (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.4

Combine the numerators over the common denominator.

$10 \frac{20 (b + 220) - 20 (b - 20)}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.5

Simplify the numerator.

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Step 2.1.5.1

Factor $20$ out of $20 (b + 220) - 20 (b - 20)$ .

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Step 2.1.5.1.1

Factor $20$ out of $- 20 (b - 20)$ .

$10 \frac{20 (b + 220) + 20 (- (b - 20))}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.5.1.2

Factor $20$ out of $20 (b + 220) + 20 (- (b - 20))$ .

$10 \frac{20 (b + 220 - (b - 20))}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.5.2

Apply the distributive property.

$10 \frac{20 (b + 220 - b - - 20)}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.5.3

Multiply $- 1$ by $- 20$ .

$10 \frac{20 (b + 220 - b + 20)}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.5.4

Subtract $b$ from $b$ .

$10 \frac{20 (0 + 220 + 20)}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.5.5

Add $0$ and $220$ .

$10 \frac{20 (220 + 20)}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.5.6

Add $220$ and $20$ .

$10 \frac{20 \cdot 240}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.6

Multiply $20$ by $240$ .

$10 \frac{4800}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.7

Multiply $10 \frac{4800}{b - 20}$ .

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Step 2.1.7.1

Combine $10$ and $\frac{4800}{b - 20}$ .

$\frac{10 \cdot 4800}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.7.2

Multiply $10$ by $4800$ .

$\frac{48000}{b - 20} (b - 2 \cdot 10) - 48000 = 0$

Step 2.1.8

Multiply $- 2$ by $10$ .

$\frac{48000}{b - 20} (b - 20) - 48000 = 0$

Step 2.1.9

Cancel the common factor of $b - 20$ .

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Step 2.1.9.1

Cancel the common factor.

$\frac{48000}{b - 20} (b - 20) - 48000 = 0$

Step 2.1.9.2

Rewrite the expression.

$48000 - 48000 = 0$

Step 2.2

Subtract $48000$ from $48000$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true