Precalculus Examples

$- \frac{12 P}{0.024} = e^{0.24} \cdot (56000 - \frac{12 P}{0.024})$

Step 1

Multiply both sides by $0.024$ .

$- \frac{12 P}{0.024} \cdot 0.024 = e^{0.24} \cdot (56000 - \frac{12 P}{0.024}) \cdot 0.024$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $0.024$ .

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Step 2.1.1.1

Move the leading negative in $- \frac{12 P}{0.024}$ into the numerator.

$\frac{- 12 P}{0.024} \cdot 0.024 = e^{0.24} \cdot (56000 - \frac{12 P}{0.024}) \cdot 0.024$

Step 2.1.1.2

Cancel the common factor.

$\frac{- 12 P}{0.024} \cdot 0.024 = e^{0.24} \cdot (56000 - \frac{12 P}{0.024}) \cdot 0.024$

Step 2.1.1.3

Rewrite the expression.

$- 12 P = e^{0.24} \cdot (56000 - \frac{12 P}{0.024}) \cdot 0.024$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $e^{0.24} \cdot (56000 - \frac{12 P}{0.024}) \cdot 0.024$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Factor $12$ out of $12 P$ .

$- 12 P = e^{0.24} \cdot (56000 - \frac{12 (P)}{0.024}) \cdot 0.024$

Step 2.2.1.1.2

Factor $0.024$ out of $0.024$ .

$- 12 P = e^{0.24} \cdot (56000 - \frac{12 (P)}{0.024 (1)}) \cdot 0.024$

Step 2.2.1.1.3

Separate fractions.

$- 12 P = e^{0.24} \cdot (56000 - (\frac{12}{0.024} \cdot \frac{P}{1})) \cdot 0.024$

Step 2.2.1.1.4

Divide $12$ by $0.024$ .

$- 12 P = e^{0.24} \cdot (56000 - (500 \frac{P}{1})) \cdot 0.024$

Step 2.2.1.1.5

Divide $P$ by $1$ .

$- 12 P = e^{0.24} \cdot (56000 - (500 P)) \cdot 0.024$

Step 2.2.1.1.6

Multiply $500$ by $- 1$ .

$- 12 P = e^{0.24} \cdot (56000 - 500 P) \cdot 0.024$

Step 2.2.1.2

Simplify by multiplying through.

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Step 2.2.1.2.1

Apply the distributive property.

$- 12 P = (e^{0.24} \cdot 56000 + e^{0.24} (- 500 P)) \cdot 0.024$

Step 2.2.1.2.2

Move $56000$ to the left of $e^{0.24}$ .

$- 12 P = (56000 \cdot e^{0.24} + e^{0.24} (- 500 P)) \cdot 0.024$

Step 2.2.1.2.3

Apply the distributive property.

$- 12 P = 56000 e^{0.24} \cdot 0.024 + e^{0.24} (- 500 P) \cdot 0.024$

Step 2.2.1.3

Multiply $56000 e^{0.24} \cdot 0.024$ .

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Step 2.2.1.3.1

Multiply $0.024$ by $56000$ .

$- 12 P = 1344 e^{0.24} + e^{0.24} (- 500 P) \cdot 0.024$

Step 2.2.1.3.2

Multiply $1344$ by $e^{0.24}$ .

$- 12 P = 1708.55885803 + e^{0.24} (- 500 P) \cdot 0.024$

Step 2.2.1.4

Multiply $e^{0.24} (- 500 P) \cdot 0.024$ .

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Step 2.2.1.4.1

Multiply $0.024$ by $e^{0.24}$ .

$- 12 P = 1708.55885803 + 0.03050997 (- 500 P)$

Step 2.2.1.4.2

Multiply $- 500$ by $0.03050997$ .

$- 12 P = 1708.55885803 - 15.2549898 P$

Step 2.2.1.5

Reorder $1708.55885803$ and $- 15.2549898 P$ .

$- 12 P = - 15.2549898 P + 1708.55885803$

Step 3

Solve for $P$ .

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Step 3.1

Move all terms containing $P$ to the left side of the equation.

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Step 3.1.1

Add $15.2549898 P$ to both sides of the equation.

$- 12 P + 15.2549898 P = 1708.55885803$

Step 3.1.2

Add $- 12 P$ and $15.2549898 P$ .

$3.2549898 P = 1708.55885803$

Step 3.2

Divide each term in $3.2549898 P = 1708.55885803$ by $3.2549898$ and simplify.

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Step 3.2.1

Divide each term in $3.2549898 P = 1708.55885803$ by $3.2549898$ .

$\frac{3.2549898 P}{3.2549898} = \frac{1708.55885803}{3.2549898}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3.2549898$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3.2549898 P}{3.2549898} = \frac{1708.55885803}{3.2549898}$

Step 3.2.2.1.2

Divide $P$ by $1$ .

$P = \frac{1708.55885803}{3.2549898}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $1708.55885803$ by $3.2549898$ .

$P = 524.90451921$