Finite Math Examples

$c = \frac{9}{2} \cdot (k - 15)$

Step 1

Rewrite the equation as $\frac{9}{2} \cdot (k - 15) = c$ .

$\frac{9}{2} \cdot (k - 15) = c$

Step 2

Multiply both sides of the equation by $\frac{2}{9}$ .

$\frac{2}{9} (\frac{9}{2} \cdot (k - 15)) = \frac{2}{9} c$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{2}{9} (\frac{9}{2} \cdot (k - 15))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{2}{9} (\frac{9}{2} k + \frac{9}{2} \cdot - 15) = \frac{2}{9} c$

Step 3.1.1.2

Combine $\frac{9}{2}$ and $k$ .

$\frac{2}{9} (\frac{9 k}{2} + \frac{9}{2} \cdot - 15) = \frac{2}{9} c$

Step 3.1.1.3

Multiply $\frac{9}{2} \cdot - 15$ .

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Step 3.1.1.3.1

Combine $\frac{9}{2}$ and $- 15$ .

$\frac{2}{9} (\frac{9 k}{2} + \frac{9 \cdot - 15}{2}) = \frac{2}{9} c$

Step 3.1.1.3.2

Multiply $9$ by $- 15$ .

$\frac{2}{9} (\frac{9 k}{2} + \frac{- 135}{2}) = \frac{2}{9} c$

Step 3.1.1.4

Move the negative in front of the fraction.

$\frac{2}{9} (\frac{9 k}{2} - \frac{135}{2}) = \frac{2}{9} c$

Step 3.1.1.5

Apply the distributive property.

$\frac{2}{9} \cdot \frac{9 k}{2} + \frac{2}{9} (- \frac{135}{2}) = \frac{2}{9} c$

Step 3.1.1.6

Cancel the common factor of $2$ .

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Step 3.1.1.6.1

Cancel the common factor.

$\frac{2}{9} \cdot \frac{9 k}{2} + \frac{2}{9} (- \frac{135}{2}) = \frac{2}{9} c$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{9} (9 k) + \frac{2}{9} (- \frac{135}{2}) = \frac{2}{9} c$

Step 3.1.1.7

Cancel the common factor of $9$ .

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Step 3.1.1.7.1

Factor $9$ out of $9 k$ .

$\frac{1}{9} (9 (k)) + \frac{2}{9} (- \frac{135}{2}) = \frac{2}{9} c$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{9} (9 k) + \frac{2}{9} (- \frac{135}{2}) = \frac{2}{9} c$

Step 3.1.1.7.3

Rewrite the expression.

$k + \frac{2}{9} (- \frac{135}{2}) = \frac{2}{9} c$

Step 3.1.1.8

Cancel the common factor of $2$ .

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Step 3.1.1.8.1

Move the leading negative in $- \frac{135}{2}$ into the numerator.

$k + \frac{2}{9} \cdot \frac{- 135}{2} = \frac{2}{9} c$

Step 3.1.1.8.2

Cancel the common factor.

$k + \frac{2}{9} \cdot \frac{- 135}{2} = \frac{2}{9} c$

Step 3.1.1.8.3

Rewrite the expression.

$k + \frac{1}{9} \cdot - 135 = \frac{2}{9} c$

Step 3.1.1.9

Cancel the common factor of $9$ .

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Step 3.1.1.9.1

Factor $9$ out of $- 135$ .

$k + \frac{1}{9} \cdot (9 (- 15)) = \frac{2}{9} c$

Step 3.1.1.9.2

Cancel the common factor.

$k + \frac{1}{9} \cdot (9 \cdot - 15) = \frac{2}{9} c$

Step 3.1.1.9.3

Rewrite the expression.

$k - 15 = \frac{2}{9} c$

Step 3.2

Simplify the right side.

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Step 3.2.1

Combine $\frac{2}{9}$ and $c$ .

$k - 15 = \frac{2 c}{9}$

Step 4

Add $15$ to both sides of the equation.

$k = \frac{2 c}{9} + 15$