Calculus Examples

$2 = \frac{2000}{3 (150) + 50} + C$

Step 1

Rewrite the equation as $\frac{2000}{3 (150) + 50} + C = 2$ .

$\frac{2000}{3 (150) + 50} + C = 2$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $2000$ and $3 (150) + 50$ .

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Step 2.1.1

Factor $50$ out of $2000$ .

$\frac{50 \cdot 40}{3 (150) + 50} + C = 2$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $50$ out of $3 (150)$ .

$\frac{50 \cdot 40}{50 (3 \cdot (3)) + 50} + C = 2$

Step 2.1.2.2

Factor $50$ out of $50$ .

$\frac{50 \cdot 40}{50 (3 \cdot (3)) + 50 (1)} + C = 2$

Step 2.1.2.3

Factor $50$ out of $50 (3 \cdot (3)) + 50 (1)$ .

$\frac{50 \cdot 40}{50 (3 \cdot (3) + 1)} + C = 2$

Step 2.1.2.4

Cancel the common factor.

$\frac{50 \cdot 40}{50 (3 \cdot (3) + 1)} + C = 2$

Step 2.1.2.5

Rewrite the expression.

$\frac{40}{3 \cdot (3) + 1} + C = 2$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $3$ by $3$ .

$\frac{40}{9 + 1} + C = 2$

Step 2.2.2

Add $9$ and $1$ .

$\frac{40}{10} + C = 2$

Step 2.3

Divide $40$ by $10$ .

$4 + C = 2$

Step 3

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

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Step 3.1

Subtract $4$ from both sides of the equation.

$C = 2 - 4$

Step 3.2

Subtract $4$ from $2$ .

$C = - 2$