Finite Math Examples

$D (5) = \frac{21 r + 10}{20}$

Step 1

Rewrite the equation as $\frac{21 r + 10}{20} = D (5)$ .

$\frac{21 r + 10}{20} = D (5)$

Step 2

Multiply both sides by $20$ .

$\frac{21 r + 10}{20} \cdot 20 = D (5) \cdot 20$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $20$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{21 r + 10}{20} \cdot 20 = D (5) \cdot 20$

Step 3.1.1.2

Rewrite the expression.

$21 r + 10 = D (5) \cdot 20$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $D (5) \cdot 20$ .

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Step 3.2.1.1

Move $5$ to the left of $D$ .

$21 r + 10 = 5 D \cdot 20$

Step 3.2.1.2

Multiply $20$ by $5$ .

$21 r + 10 = 100 D$

Step 4

Solve for $r$ .

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Step 4.1

Subtract $10$ from both sides of the equation.

$21 r = 100 D - 10$

Step 4.2

Divide each term in $21 r = 100 D - 10$ by $21$ and simplify.

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Step 4.2.1

Divide each term in $21 r = 100 D - 10$ by $21$ .

$\frac{21 r}{21} = \frac{100 D}{21} + \frac{- 10}{21}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $21$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{21 r}{21} = \frac{100 D}{21} + \frac{- 10}{21}$

Step 4.2.2.1.2

Divide $r$ by $1$ .

$r = \frac{100 D}{21} + \frac{- 10}{21}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$r = \frac{100 D}{21} - \frac{10}{21}$