Finite Math Examples

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

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

Step 1

Subtract

48000

$48000$ from both sides of the equation.

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

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

Step 2

Simplify

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

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

- 2

$- 2$ by

10

$10$ .

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

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

Step 2.1.2

To write

- 20

$- 20$ as a fraction with a common denominator, multiply by

\frac{b - 20}{b - 20}

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

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

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

Step 2.1.3

Combine

- 20

$- 20$ and

\frac{b - 20}{b - 20}

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

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

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

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

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

Step 2.1.5

Simplify the numerator.

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Step 2.1.5.1

Factor

20

$20$ out of

20 (b + 220) - 20 (b - 20)

$20 (b + 220) - 20 (b - 20)$ .

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Step 2.1.5.1.1

Factor

20

$20$ out of

- 20 (b - 20)

$- 20 (b - 20)$ .

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

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

Step 2.1.5.1.2

Factor

20

$20$ out of

20 (b + 220) + 20 (- (b - 20))

$20 (b + 220) + 20 (- (b - 20))$ .

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

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

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

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

Step 2.1.5.2

Apply the distributive property.

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

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

Step 2.1.5.3

Multiply

- 1

$- 1$ by

- 20

$- 20$ .

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

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

Step 2.1.5.4

Subtract

b

$b$ from

b

$b$ .

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

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

Step 2.1.5.5

Add

0

$0$ and

220

$220$ .

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

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

Step 2.1.5.6

Add

220

$220$ and

20

$20$ .

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

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

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

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

Step 2.1.6

Multiply

20

$20$ by

240

$240$ .

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

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

Step 2.1.7

Multiply

10 \frac{4800}{b - 20}

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

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Step 2.1.7.1

Combine

10

$10$ and

\frac{4800}{b - 20}

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

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

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

Step 2.1.7.2

Multiply

10

$10$ by

4800

$4800$ .

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

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

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

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

Step 2.1.8

Multiply

- 2

$- 2$ by

10

$10$ .

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

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

Step 2.1.9

Cancel the common factor of

b - 20

$b - 20$ .

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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