Finite Math Examples

$r = M θ - N^{0} (1 + r)$

Step 1

Simplify each term.

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Step 1.1

Anything raised to $0$ is $1$ .

$r = M θ - 1 \cdot 1 (1 + r)$

Step 1.2

Multiply $- 1$ by $1$ .

$r = M θ - 1 (1 + r)$

Step 1.3

Apply the distributive property.

$r = M θ - 1 \cdot 1 - 1 r$

Step 1.4

Multiply $- 1$ by $1$ .

$r = M θ - 1 - 1 r$

Step 1.5

Rewrite $- 1 r$ as $- r$ .

$r = M θ - 1 - r$

Step 2

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

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Step 2.1

Add $r$ to both sides of the equation.

$r + r = M θ - 1$

Step 2.2

Add $r$ and $r$ .

$2 r = M θ - 1$

Step 3

Divide each term in $2 r = M θ - 1$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 r = M θ - 1$ by $2$ .

$\frac{2 r}{2} = \frac{M θ}{2} + \frac{- 1}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 r}{2} = \frac{M θ}{2} + \frac{- 1}{2}$

Step 3.2.1.2

Divide $r$ by $1$ .

$r = \frac{M θ}{2} + \frac{- 1}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$r = \frac{M θ}{2} - \frac{1}{2}$